My Research Group in TIFR

Vikram Tripathi

Professor of Physics
Department of Theoretical Physics

Tata Institute of Fundamental Research

I am a condensed matter theorist and my research area is strongly correlated quantum systems. You can find my CV here.

Research

My current focus is on low-dimensional Mott insulator systems, especially quantum spin liquids and topologically ordered phases. Over a longer time scale, I have also worked extensively on disordered mesoscopic systems and spin-orbit materials.

Besides strongly correlated quantum systems, I am very interested in practical problems such as hybrid Classical-Quantum Algorithms for solving large scale Linear Equation systems, and exploring new "better-than-nature" strategies for manipulating the flocking behaviour of large autonomous swarms. These are ongoing works.

Recent significant developments involving my research group include

(i) discovery of impurity-induced nonabelian anyons in Kitaev spin liquids,

(ii) developing lattice matter-Chern-Simons (CS) gauge theories from microscopic spin-1/2 models on arbitrary 2D lattices, understanding excitations and finite temperature response of abelian and nonabelian topological phases in some of these matter-CS theories,

(iii) development of new numerical techniques, e.g., using information-theoretic ideas for characterizing quasiparticles and their stability in quantum many-body systems, and adapting purification-based tensor network strategies for calculating the thermal Hall response and chiral central charge of gapped 2D spin systems, and

(iv) charge BKT theory of Vogel-Fulcher type finite temperature insulator transitions in strongly disordered 2D superconductors.

Click on the collapsible items below to learn more about what we do.

(a) Kitaev systems

The honeycomb Kitaev model occupies a paradigmatic place in condensed matter - it describes a deconfined topologically ordered phase that may be abelian (Z2, chiral) or non-abelian (Ising) depending on the parameter regime. This is an example of a quantum spin liquid (QSL) - highly entangled quantum states that remain disordered even at zero temperature, and these systems exhibit fractionalized excitations. Experimental realization of a Kitaev spin liquid has proven elusive.

Our group has made significant contributions towards understanding the physics of Kitaev systems. These include the discovery [PRL2010, PRB2016] of a new mechanism for realizing non-abelian anyons through engineering defects in the Kitaev model, extensive modelling of high field magneto-torque data for exploring the possibility of field-induced spin liquids in Kitaev materials [PRB(R)2019], developing new theoretical tools based on many-body localization in the Hilbert space for understanding quasiparticle stability in perturbed Kitaev systems [PRB(R)2020] and new numerical techniques for studying the thermal Hall response of gapped many-body systems [PRB(L)2023, Editor's Suggestion]. Some research highlights are described below.

Vacancies and spin impurities as non-abelian anyons

In 2010, our group discovered [PRL2010, PRB2016] a new mechanism for creating non-abelian anyons by engineering defects, e.g. freezing local moments in the Kitaev system with an STM tip. This opens a way for future anyon braiding operations for topological quantum computing.

Magneto-torque response studies and field-induced spin liquid

Known Kitaev materials, e.g. Na2IrO3 and α-RuCl3, are magnetically ordered. Intense efforts, such as the landmark 2018 claim (now challenged) of half-quantized thermal Hall effect in α-RuCl3, are underway to find if Kitaev physics could still be accessed, for example, through field-suppression of magnetic order. In this context, we collaborated with Prof. S. Sebastian's group in Cambridge, where they had observed very unusual features in the high-field torque data on Na2IrO3.

Our calculations showed [PRB(R)2019] that the torque data could be reconciled only with ferromagnetic Kitaev interactions, and provided evidence that key features in the torque response were attributable to field-suppression of magnetic order into a phase with short-range spin correlations.

However the study left open the question whether this was a field-revived Ising topological ordered state. Reviving a Kitaev spin liquid by field suppression of magnetic order is still an open question.

Kitaev physics in the presence of competing interactions

Subsequently, to identify parameter regimes that could host Kitaev excitations, we developed a theory [PRB(R)2020] of quasiparticle stability using ideas of localization in the many-body Hilbert space (MBL).

The challenging calculation requiring tens of thousands of excited states in 32-spin systems was accomplished with FEAST eigensolvers.

Surprisingly, low-lying Kitaev quasiparticles were found to be stable against interaction-induced decay for quite some distance within the magnetically ordered phase abutting the spin liquid phase.

Recently, in collaboration with Prof. Subir Sachdev (Harvard), the MBL strategy for quasiparticle stability was extended to the SYK t-J model of the cuprates.

The study [PRB(L)2022] not only confirmed earlier field-theoretical calculations by Sachdev and others, but also demonstrated the stability of a new spinless (Jordan-Wigner) fermion on the underdoped side.

This could be relevant for understanding the mysterious large thermal Hall response in underdoped cuprates.

Thermal Hall response

Our group has recently developed a quasiparticle-agnostic purification-based finite temperature approach for the thermal Hall response of 2D gapped spin systems on arbitrary lattices.

The numerical approach is designed to work even in parameter regimes where quasiparticles are either not known or do not exist.

The study revealed a large non-quantized thermal Hall response in Kitaev systems near field suppressed magnetic order [PRB(L)2023, Editor's Suggestion] but no measurable signature of topological order, casting doubt on the original experimental claim but in supporting the conclusions of other experimental groups that reported large non-quantized thermal Hall response in the vicinity of field-suppressed magnetic order.

More generally, our technique provides one of the earliest direct numerical calculations of the chiral central charge that governs low-temperature thermal Hall response.

(b) Lattice gauge theories of topological matter

In condensed matter systems, lattice quantum spin-1/2 degrees of freedom are neither fermionic nor bosonic and their field theories are usually lattice matter gauge theories. Where the gauge theories are derived from microscopic spin models, their analysis can give us a complete understanding of the nature of the phases (e.g. topological, magnetically ordered, deconfined) and their excitations (e.g. anyons) often where contemporary numerical approaches fail.

We developed analytical lattice matter Chern-Simons gauge approaches for understanding excitations and finite temperature properties of time-reversal symmetry broken gapped phases of honeycomb Kitaev and Kagome Heisenberg antiferromagnet models.

Field-tuned topological transitions in the Kitaev model

We recently developed [PRB2023,PRBLett.2025] (using a new Jordan-Wigner fermionization strategy) mutual Chern-Simons gauge theories for spin-1/2 systems on arbitrary 2D lattices. Using an enlarged Hilbert space that included the dual lattice gauge fields, we obtained a consistent formulation of Chern-Simons theories for spin-1/2 models on 2D lattices lacking one-to-one face-vertex correspondence. This overcame a longstanding “no-go theorem” of Fradkin that turned out to be a consequence of their using only a single gauge field.

Using this approach, a complete characterization of the different phases and emergent excitations of a field-tuned isotropic Kitaev model in different field regimes has been obtained. These include the ground state degeneracy, topological entanglement entropy, chiral central charge, emergent excitations and their braiding rules in different field regimes. Both ferromagnetic and antiferromagnetic signs of the Kitaev coupling were studied.

For the antiferro case, there are strongly divergent views in the literature about the nature of the spin liquid and topological order at intermediate fields (see e.g. our 2024 topical review). Such studies are either based on exact diagonalization or DMRG based numerical studies that suffer from finite size limitations, or parton mean field analyses that ignore the crucial contribution of the gauge degrees of freedom.

Our calculations show a low-field nonabelian (Ising topological order) ITO phase for both ferro and antiferro sign of Kitaev interactions – this incidentally provides the first proof of Kitaev’s original 2006 proposal of an ITO phase in the low-field regime of the isotropic Kitaev model.

We found that in the antiferro case, the intermediate field phase is essentially an abelian non-invertible topological phase with chiral central charge c=1/2, incidentally the same value as the ITO. Thus both the low and intermediate field regimes in the AFM Kitaev model are chiral spin liquids but only the former has ITO. Despite the lack of topological order in this intermediate phase, thermal Hall conductivity continues to be half-quantized and thus should not be used as a smoking gun test for ITO experimentally.

For strong Zeeman fields along a (z-)spin quantization direction, there is no topological order but the properties are still quite interesting. Jagannath maps the spin model to a gauged superconductor with a mutual (Z2 x Z2) Maxwell-Chern-Simons gauge action. As the Zeeman field is increased, the superconductivity gets degraded through the proliferation of link instantons (phase fluctuation mechanism). The study revealed that the dispersion of the gauge fields undergoes a dimensional reduction from 2D-like to 1D-like with increasing field.

Gauge theory of thermal Hall response of a chiral spin liquid

This work [preprint] is in collaboration with Prof. Subir Sachdev (Harvard) and Dr. Haoyu Guo (Cornell).

Thermal transport has emerged as a valuable tool for probing the fractionalized excitations in quantum spin liquids. However validating the low temperature quantized thermal Hall response of topological phases has been challenging and controversial. The finite temperature behavior, especially in the quantum critical regime above the spectral gap, can provide useful signatures of the underlying topological order. Motivated thus, we studied the spin-1/2 Heisenberg antiferromagnet on a kagome lattice that is widely believed to be a U(1) Dirac spin liquid. Scalar spin chirality perturbations turn this into a gapped abelian chiral spin liquid (CSL) with semionic topological order. Using a recently developed large-N technique, we obtained explicit expressions for the thermal Hall conductivity at finite temperatures taking into account both matter and gauge fluctuations. At low temperatures below the spectral gap, the quantized thermal Hall response agrees with that expected from conformal field theory and gravitational anomaly arguments. Our main finding is that in a large temperature window spanning the spectral gap and the Curie temperature scales where quantum critical fluctuations dominate, the thermal Hall conductivity follows a power-law with logarithmic corrections. The analysis also provides a route to understanding the thermal Hall response at temperatures in the quantum critical regime of other spin liquid phases.

(c) Fast preparation and measurement resilience of topologically ordered states

Anyons in topologically ordered systems are also interesting from the applications perspective as their braiding realizes error correcting quantum gates. There are two practical challenges: fast preparation of topologically ordered states with high fidelity, and resilience of the information encoded in states with different topological orders to local random projective measurements.

We are working on both these aspects. Where the topologically ordered states are known to be gapped ground states of some local Hamiltonians, we have proposed [PRB2021] counterdiabatic strategies that can speed up state preparation by factors of more than a million compared to comparable adiabatic protocols.

For measurement resilience of quantum information in topologically ordered states, we considered the Kitaev model, where the ground states may have abelian (Z2) or nonabelian (ITO) topological order depending on the parameter regime. Our protocol consists of Unitary (Hamiltonian) evolution interrupted by local projective measurements. We found [PRB(L)2024] that when measured by a tripartite mutual information (equivalent to the topological entanglement entropy for states that are described by a topological QFT), the state with nonabelian ITO shows far greater resilience when subjected to this protocol.

Read on to learn more.

Fast preparation of a topologically ordered state

A standard way to prepare a desired quantum state beginning with a trivial product state is to use an adiabatic protocol. The speed at which the state can be prepared by adiabatic protocols is limited by Landau-Zener tunnelling to excited states - a process similar to pair production by the Schwinger mechanism.

Counterdiabatic (CD) or "shortcut to adiabaticity" protocols are designed to suppresses transitions to excited state through destructive interference effects associated with the Berry phase through the addition of suitable time-dependent counter-terms to the Hamiltonian. These counter-terms generically induce nonlocal interactions of many spins. However, a “local” truncation of the CD counter-term is easily engineered by elastic strain. Despite the truncation, we showed [PRB2021] a high fidelity preparation of the topologically ordered ground state is possible with speeds as much as a million times faster compared to adiabatic protocols.

Measurement resilience of quantum information in topologically ordered state

We investigated [PRB(L)2024] the fragility of quantum information in two topologically ordered states (associated with two different parameter regimes of the Kitaev model) under a protocol consisting of Unitary (Hamiltonian) evolution interrupted by random local projective measurements of the spins. For this, we used the tripartite mutual information γ – equivalent to the topological entanglement entropy for topologically ordered states – as a measure.

We showed that in the steady state, γ remained significant up to high measurement rates per site r comparable to the energy per site when the initial state has Ising topological order (ITO), beyond which it degrades with increasing r.

We contrasted this with the abelian Z2 topologically ordered ground state in the Toric Code regime of the Kitaev model with the same energy, which has garnered greater attention in the literature of fault-tolerant quantum computation. We observed that γ in the Toric Code regime of the Kitaev model collapsed rapidly beyond very small values of r. The collapse of γ at very small measurement rates is reminiscent of recent work showing that the topological order of the Toric Code ground state gets degraded when subjected to arbitrarily small temperatures.

Physically, the degradation of γ is on account of vison excitations. We also found that at high measurement rates, while topological order was lost, expectation of certain local observables have distinct signatures of the initial quantum state, thus providing a diagnostic of topological order.

(d) Nonequilibrium response of driven open Mott systems

Driven Mott insulators exhibit diverse phenomena that may not be present in their equilibrium or linear response regimes such as nonequilibrium insulator-metal transitions, Bloch oscillations (Wannier-Stark quantization), current enhanced diamagnetism, and even a novel (eta-pairing) superconductivity. Nonequilibrium steady states (NESS) are possible only for open (dissipative) systems. Our interest is in understanding the nature of the NESS and the approach to such states.

In my group, we have approached the problem of far from equilibrium response of open Mott systems in two different ways: (i) a large-N Keldysh field theoretical treatment, and (ii) analysis of an effective PT-symmetric non-Hermitian model. The former gives us an understanding of both the NESS and the approach to it but is technically challenging to implement. The latter gives an understanding of only the NESS and its application too is more restrictive; however, the analysis is much simpler than Keldysh field theory.

An important finding we made using the Keldysh treatment [PRB2019] is that the (ergodic) NESS state is established on a time scale that is inversely proportional to the nonequilibrium temperature, which translates to a power-law (not exponential) dependence of the relaxation time on the number of bath degrees of freedom accessible locally.

The ac response [PRB2020] is no less interesting - at sufficiently high frequencies, the ac response is reminiscent of an eta-pairing Josephson array. However, when a dc field is simultaneously applied, the smoking gun signature of a supercurrent - Shapiro steps - are completely absent. This shows that the superconductor-like ac current response is a consequence of number-phase uncertainty effects that are common to superconductor Josephson arrays as well as our quantum dot system.

The PT-symmetry theory was developed in collaboration with Prof. Valerii Vinokur (Argonne). We showed [PRB(R)2016,SciRep2020] that the nonequilibrium Mott insulator to metal transition proceeds through pair (particle-hole) production by the Landau-Zener mechanism, and that the transition is associated with an exceptional point at which PT-symmetry gets broken.

More details below.

Approach to equilibrium: Keldysh theory

It is well-known that in the absence of dissipation, a regular one-dimensional Mott insulator does not give a dc current steady state response to a uniform electric field, but instead exhibits Bloch oscillations, indefinitely, due to discreteness of the Wannier-Stark spectrum. Dissipation is crucial for realizing a steady state dc response.

The approach to a nonequilibrium dc current state can be very nontrivial. Existing treatments of nonequilibrium response of dissipative Mott insulators are usually based on numerical dynamical mean field theory (DMFT) calculations (e.g. papers by the Kotliar or Werner groups). Here we proposed a new analytic approach to this problem.

We developed an effective large-N Keldysh field theory approach [PRB2019] for studying nonequilibrium transport in a regular one -dimensional Mott insulator system consisting of an array of mesoscopic quantum dots. Transport is governed by the interplay of interdot tunneling and Coulomb blockade. In our model, large-N (which is of the order of the number of conduction electrons in each mesoscopic dot) appears both as a source of dissipation (Landau damping) and incoherent Fermi Golden Rule type hopping transport, as well as enabling a systematic 1/N expansion for a controlled analytical treatment even in the vicinity of the Mott insulator-metal transition where there are no other small parameters.

We found that in the presence of dissipation, the Bloch oscillations of current decay on a time scale that is essentially the inverse nonequilibrium temperature of the dots, ultimately leading to the steady state dc response (an ergodic state). Remarkably, we found that this timescale for establishing NESS grows as a power-law in N, implying that quantum coherence effects get erased and ergodicity is established on a time scale that diverges polynomially and not exponentially in system size.

Superconductor-like ac response

A number of recent studies of optically excited Mott insulating half-filled Hubbard models have proposed a new route to superconductivity through doublon creation, possibly an exotic eta-pairing state. However these half-filled Hubbard models are special since charge excitations necessarily create doublons (local Cooper pairs). Our open Mott-insulator system consisting of a mesoscopic quantum dot array does not suffer from this problem, and is designed not to have a superconductor phase.

We found [PRB2020] that deep in the Mott insulator regime, the NESS response of the ac driven quantum dot array shows numerous similarities with a resistively shunted Josephson array. A nonequilibrium Mott insulating to conductor transition is observed as the drive frequency is increased. The diamagnetic component of the NESS in the conducting phase is anomalous, implying negative inductance, strikingly reminiscent of the eta-pairing phase of a Josephson array with negative phase stiffness. However in the presence of an additional DC field, the signature of supercurrent - Shapiro steps - is completely absent.

We interpreted these properties as number-phase fluctuation effects shared with Josephson systems rather than a manifestation of eta-pairing superconductivity. Since in the literature, the diamagnetic stiffness is used as a diagnosis of eta-pairing superconductivity in optically excited half-filled Hubbard chains, our findings serve as a caution here.

Fast scrambling

Subsequently, in order to understand the connection between dissipation and scrambling, we explored, using the same Keldysh formalism, the nonequilibrium current response and its relation to certain out of time ordered correlators (OTOCs). We showed that the amplitude of Bloch-like oscillations decreases exponentially at long times, with a universal exponent, 2πkT/ℏ associated with fast scramblers. Our Mott insulator model provides a new example of a fast scrambler in addition to the extremal black holes and the Sachdev-Ye-Kitaev (SYK) model.

PT-symmetry breaking and the nonequilibrium Mott transition

The theory was was develped in collaboration with Prof. Valerii Vinokur's group in Argonne. These ideas were confirmed in joint experiment-theory work on current driven superconductor-metal transitions in Au-nanopatterned arrays on superconducting substrates. The experiments were conducted by Dr. Nicola Poccia in Harvard.

On the theoretical side, we mapped [SciRep2020] a nonequilibrium Hubbard chain coupled to a phonon bath to an equivalent PT-symmetric non-Hermitian Hubbard model, which, we had argued earlier [PRB(R)2016], was a paradigm for the dynamic Mott transition.

The transition is associated with PT-symmetry breaking. Bethe ansatz and DMFT calculations in the paper were perfomed in TIFR. The theory was then confirmed experimentally [PRB(R)2017].

(e) Strongly disordered low-dimensional superconductors

Potential disorder diminishes Coulomb screening, and the resulting reduced mobility of electrons enhances electromagnetic phase fluctuations. Proliferation of phase fluctuations degrades superconductivity even as Cooper pairing may exist locally. In the normal state in two dimensions, phase fluctuations may even drive a finite temperature transition to a perfectly insulating "superinsulator" state.

Our group has made important contributions towards understanding phase fluctuation effects in superconductors.

Over a five-year long experiment-theory collaboration with Prof. Raychaudhuri in TIFR (2008-12), we proved the dominant role of phase (pair) fluctuations in the degradation of 2D superconductivity at strong (weak) disorder [PRB2008, PRL2011, PRB2012].

In subsequent theoretical work (2013-18), my group developed a unified framework based on phase-disordered Josephson-junction models that capture two intriguing experimental phenomena in 2D in the normal state - (i) colossal magnetoresistance and (ii) the finite temperature (super-)insulator transition - as manifestations respectively of vortex [PRB2016] and charge [PRB(R)2017] disordered Berezinskii-Kosterlitz-Thouless (BKT) physics. In the former case (i), we also obtained the field dependence of superfluid stiffness, which can be verified by penetration depth measurements. We showed in (ii) that strong disorder fundamentally alters BKT criticality to a more singular Vogel-Fulcher-Tammann (VFT) glassy behaviour seen in experiments. The charge BKT and VFT theory was developed in collaboration with Prof. Valerii Vinokur (Argonne).

Disorder also strongly affects Andreev transport in SN junctions, potentially impacting tunnelling spectroscopy. In this collaboration with Prof. Kedar Damle (TIFR) and the group of Prof. Satya Majumdar (Univ. Paris Sud), we used Random Matrix Theory techniques, to obtain [PRL2011] the full Andreev conductance distribution of wide junctions, revealing multiple high-order phase transitions away from the mean Andreev conductance. These features illustrate how quantum interference effects may impact the Andreev conductance of SN junctions.

(f) Dynamics of mesoscopic systems

Contemporary semiconductor technology is planar as it affords easy tunability of electronic properties using electrostatic gates. The low-dimensionality provides a natural setting for exploring new phenomena since the effects of disorder (inevitable in any system) as well as quantum mechanics (e.g. quantization, interference) get significantly enhanced.

My group has worked extensively in this very broad area.

Some of the significant contributions of our group include development of a theory of NMR in semiconductor Kondo lattices [PRL2009], magnetoresistance [PRB2006, PRB2011] and intrinsic Hall effect [SciRep2015] in insulating semiconductor heterostructures, charge transport in disordered graphene superlattices [NanoLett2013], and detection of CDW transitions through high-frequency elastic properties of nano-electromechanical devices [PRL2013]. Some of this work has involved close experiment-theory collaboration involving P. B. Littlewood (Argonne/Uchicago), M. Deshmukh (TIFR), B. Aronzon and K. Kugel (Moscow, RAS).

Alongside our theoretical efforts towards understanding phase fluctuation effects in strongly-disordered superconductors, we have also devoted considerable attention to the phase fluctuation effects in linear response transport properties of normal granular metals. In this context we discovered [PRL2006] a strong breakdown of the Wiedemann-Franz law due to qualitatively different electronic mechanisms governing heat and charge transport.

(g) Electron correlations in spin-orbit materials

The d-block elements are characterized by strong electronic correlations and spin-orbit (SO) interactions increasing with the period, while in the f-block elements, SO interactions typically exceed correlations. Our interest has been in the intermetallics (e.g. the heavy fermion metal URu2Si2, pnictide superconductors, semi-metals CaCuSb and CaCu4As2), topological crystalline insulators (e.g. Sn-doped PbTe), and Kitaev materials (Na2IrO3).

In the area of intermetallic systems, our research has made significant impact, be it towards

(i) understanding the nature of hidden order in the heavy fermion metal URu2Si2 [NatPhys2007, JPCM2005, Nature2002] in collaboration with Profs. Piers Coleman, Premi Chandra and John Mydosh,

(ii) analysing Fe-pnictides as doped, orbital selective Mott insulators [PRB2015] in collaboration with Prof. Mukul Laad (IMSc Chennai) and Prof. Suchitra Sebastian's group in Cambridge,

(iii) predicting surface topological superconductivity in Pb-doped SnTe [PRB2017], or

(iv) searching for the 3D quantum Hall effect in the semi-metals CaCuSb and CaCu4As2 [PRB2021, PRR(L)2021] in collaboration with Prof. A. Thamizhavel's group in TIFR.

Selected Publications

Publications arranged in reverse chronological order. Click to see the list.

Avijit Maity, Haoyu Guo, Subir Sachdev, and Vikram Tripathi, Thermal Hall response of an abelian chiral spin liquid at finite temperatures, Phys. Rev. B 111, 205119 (2025). Links: journal arXiv
Jagannath Das, Aman Kumar, and Vikram Tripathi, Microscopic theory of field-tuned topological transitions in the Kitaev honeycomb model, Phys. Rev. B 111, L041111 (2025). Links: journal arXiv
Aman Kumar and Vikram Tripathi, Thermal Hall conductivity near field-suppressed magnetic order in a Kitaev-Heisenberg model, Phys. Rev. B 107, L220406 (2023). [Editor’s Suggestion] Links: journal arXiv
Sanjeev Kumar, Shekhar Sharma, and Vikram Tripathi, Counterdiabatic route for preparation of state with long-range topological order, Phys. Rev. B 104, 245113 (2021). Links: journal arXiv
Aman Kumar and V. Tripathi, Kitaev quasiparticles in a proximate spin liquid: A many-body localization perspective, Phys. Rev. B 102, 100401(R) (2020). Links: journal arXiv
S. Sankar and V. Tripathi, Keldysh field theory of a driven dissipative Mott insulator: Nonequilibrium response and phase transitions, Phys. Rev. B 99, 245113 (2019). Links: journal arXiv
Sitikantha. D Das, Sarbajaya Kundu, Zengwei Zhu, Eundeok Mun, Ross D. McDonald, Gang Li, Luis Balicas, Alix McCollam, Gang Cao, Jeffrey. G. Rau, Hae-Young Kee, Vikram Tripathi, and Suchitra E. Sebastian, Magnetic anisotropy of the alkali iridate Na2IrO3 at high magnetic fields: evidence for strong ferromagnetic Kitaev correlations, Phys. Rev. B 99, 081101(R) (2019). Links: journal arXiv
Vikram Tripathi, Alexey Galda, Himadri Barman, and Valerii M. Vinokur, Parity-time symmetry-breaking mechanism of dynamic Mott transitions in dissipative systems, Phys. Rev. B 94, 041104(R) (2016). Links: journal arXiv
S. Sengupta, N. Samudrala, V. Singh, A. Thamizhavel, P. B. Littlewood, V. Tripathi and M. M. Deshmukh, Plasmon mode modifies the elastic response of a nanoscale charge density wave system, Phys. Rev. Lett. 110, 166403 (2013). Links: journal arXiv
K. Damle, S. N. Majumdar, V. Tripathi and P. Vivo, Phase transitions in the distribution of the Andreev conductance of superconductor-metal junctions with multiple transverse modes, Phys. Rev. Lett. 107, 177206 (2011). Links: journal arXiv
V. Tripathi, Kusum Dhochak, B. A. Aronzon, V. V. Rylkov, A. B. Davydov, Bertrand Raquet, Michel Goiran and K. I. Kugel, Charge inhomogeneities and transport in semiconductor heterostructures with a manganese delta-layer, Phys. Rev. B 84, 075305 (2011). Links: journal arXiv
M. Mondal, A. Kamlapure, M. Chand, G. Saraswat, S. Kumar, J. Jesudasan, L. Benfatto, V. Tripathi and P. Raychaudhuri, Phase fluctuations in a strongly disordered s-wave superconductor close to the metal-insulator transition, Phys. Rev. Lett. 106, 047001 (2011). Links: journal arXiv
K. Dhochak, R. Shankar and V. Tripathi, Magnetic impurities in the honeycomb Kitaev model, Phys. Rev. Lett. 105, 117201 (2010). Links: journal arXiv
V. Tripathi and Y. L. Loh, Thermal conductivity of a granular metal, Phys. Rev. Lett. 96, 046805 (2006). Links: journal arXiv
P. Chandra, P. Coleman, J. A. Mydosh, and V. Tripathi, Hidden orbital order in the heavy fermion metal URu2Si2 , Nature 417, 831 (2002). Links: journal arXiv

Students and postdocs

Past graduate students

Kusum Dhochak (faculty at IIT Palakkad)
Sarath Sankar (postdoc at Tel Aviv University)
Sarbajaya Kundu (Dirac Postdoctoral Fellow at University of Florida, Gainesville)
Aman Kumar (Dirac Postdoctoral Fellow at National High Magnetic Field Lab, Tallahassee)
Sanjeev Kumar (postdoc at TU Berlin)
Jagannath Das (postdoc at Virginia Tech, Blacksburg)

Current graduate students

Avijit Maity
Ayush Sharma

Past postdoc

Himadri Barman (postdoc at National Taiwan University, Taipei, Taiwan)

Awards and honours

2014-2019: Swarnajayanti Fellowship awarded by Department of Science and Technology, Government of India

2014-15: Award from University of Chicago Center in New Delhi for Sabbatical at Argonne National Laboratory/University of Chicago

2007-2012: Ramanujan Fellowship awarded by Department of Science and Technology, Government of India

2007-2009: Associateship of the Indian Academy of Sciences, Bangalore

2002-06: Elected to Title A Fellowship of Trinity College, University of Cambridge

1996: Rouse Ball Maths Essay Prize, Trinity College, Cambridge

1994-1996: Cambridge Nehru Centenary Scholarship (awarded by the Cambridge Commonwealth Trust, University of Cambridge)

1994: R. B. Brijmohanlal Saheb Gold Medal (best performer in B.Sc. (Hons.) Physics), University of Delhi

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Vikram Tripathi

Professor of PhysicsDepartment of Theoretical Physics

Tata Institute of Fundamental Research

I am a condensed matter theorist and my research area is strongly correlated quantum systems. You can find my CV here.

Research

My current focus is on low-dimensional Mott insulator systems, especially quantum spin liquids and topologically ordered phases. Over a longer time scale, I have also worked extensively on disordered mesoscopic systems and spin-orbit materials.

Recent significant developments involving my research group include

(i) discovery of impurity-induced nonabelian anyons in Kitaev spin liquids,

(ii) developing lattice matter-Chern-Simons (CS) gauge theories from microscopic spin-1/2 models on arbitrary 2D lattices, understanding excitations and finite temperature response of abelian and nonabelian topological phases in some of these matter-CS theories,

(iv) charge BKT theory of Vogel-Fulcher type finite temperature insulator transitions in strongly disordered 2D superconductors.

Click on the collapsible items below to learn more about what we do.

(a) Kitaev systems

Vacancies and spin impurities as non-abelian anyons

In 2010, our group discovered [PRL2010, PRB2016] a new mechanism for creating non-abelian anyons by engineering defects, e.g. freezing local moments in the Kitaev system with an STM tip. This opens a way for future anyon braiding operations for topological quantum computing.

Magneto-torque response studies and field-induced spin liquid

Our calculations showed [PRB(R)2019] that the torque data could be reconciled only with ferromagnetic Kitaev interactions, and provided evidence that key features in the torque response were attributable to field-suppression of magnetic order into a phase with short-range spin correlations.

However the study left open the question whether this was a field-revived Ising topological ordered state. Reviving a Kitaev spin liquid by field suppression of magnetic order is still an open question.

Kitaev physics in the presence of competing interactions

Subsequently, to identify parameter regimes that could host Kitaev excitations, we developed a theory [PRB(R)2020] of quasiparticle stability using ideas of localization in the many-body Hilbert space (MBL).

The challenging calculation requiring tens of thousands of excited states in 32-spin systems was accomplished with FEAST eigensolvers.

Surprisingly, low-lying Kitaev quasiparticles were found to be stable against interaction-induced decay for quite some distance within the magnetically ordered phase abutting the spin liquid phase.

Recently, in collaboration with Prof. Subir Sachdev (Harvard), the MBL strategy for quasiparticle stability was extended to the SYK t-J model of the cuprates.

The study [PRB(L)2022] not only confirmed earlier field-theoretical calculations by Sachdev and others, but also demonstrated the stability of a new spinless (Jordan-Wigner) fermion on the underdoped side.

This could be relevant for understanding the mysterious large thermal Hall response in underdoped cuprates.

Thermal Hall response

Our group has recently developed a quasiparticle-agnostic purification-based finite temperature approach for the thermal Hall response of 2D gapped spin systems on arbitrary lattices.

The numerical approach is designed to work even in parameter regimes where quasiparticles are either not known or do not exist.

More generally, our technique provides one of the earliest direct numerical calculations of the chiral central charge that governs low-temperature thermal Hall response.

(b) Lattice gauge theories of topological matter

We developed analytical lattice matter Chern-Simons gauge approaches for understanding excitations and finite temperature properties of time-reversal symmetry broken gapped phases of honeycomb Kitaev and Kagome Heisenberg antiferromagnet models.

Field-tuned topological transitions in the Kitaev model

Our calculations show a low-field nonabelian (Ising topological order) ITO phase for both ferro and antiferro sign of Kitaev interactions – this incidentally provides the first proof of Kitaev’s original 2006 proposal of an ITO phase in the low-field regime of the isotropic Kitaev model.

Gauge theory of thermal Hall response of a chiral spin liquid

This work [preprint] is in collaboration with Prof. Subir Sachdev (Harvard) and Dr. Haoyu Guo (Cornell).

(c) Fast preparation and measurement resilience of topologically ordered states

Read on to learn more.

Fast preparation of a topologically ordered state

Measurement resilience of quantum information in topologically ordered state

We showed that in the steady state, γ remained significant up to high measurement rates per site r comparable to the energy per site when the initial state has Ising topological order (ITO), beyond which it degrades with increasing r.

Physically, the degradation of γ is on account of vison excitations. We also found that at high measurement rates, while topological order was lost, expectation of certain local observables have distinct signatures of the initial quantum state, thus providing a diagnostic of topological order.

(d) Nonequilibrium response of driven open Mott systems

More details below.

Approach to equilibrium: Keldysh theory

Superconductor-like ac response

Fast scrambling

PT-symmetry breaking and the nonequilibrium Mott transition

On the theoretical side, we mapped [SciRep2020] a nonequilibrium Hubbard chain coupled to a phonon bath to an equivalent PT-symmetric non-Hermitian Hubbard model, which, we had argued earlier [PRB(R)2016], was a paradigm for the dynamic Mott transition.

The transition is associated with PT-symmetry breaking. Bethe ansatz and DMFT calculations in the paper were perfomed in TIFR. The theory was then confirmed experimentally [PRB(R)2017].

(e) Strongly disordered low-dimensional superconductors

Our group has made important contributions towards understanding phase fluctuation effects in superconductors.

Over a five-year long experiment-theory collaboration with Prof. Raychaudhuri in TIFR (2008-12), we proved the dominant role of phase (pair) fluctuations in the degradation of 2D superconductivity at strong (weak) disorder [PRB2008, PRL2011, PRB2012].

(f) Dynamics of mesoscopic systems

My group has worked extensively in this very broad area.

(g) Electron correlations in spin-orbit materials

In the area of intermetallic systems, our research has made significant impact, be it towards

(i) understanding the nature of hidden order in the heavy fermion metal URu2Si2 [NatPhys2007, JPCM2005, Nature2002] in collaboration with Profs. Piers Coleman, Premi Chandra and John Mydosh,

(ii) analysing Fe-pnictides as doped, orbital selective Mott insulators [PRB2015] in collaboration with Prof. Mukul Laad (IMSc Chennai) and Prof. Suchitra Sebastian's group in Cambridge,

(iii) predicting surface topological superconductivity in Pb-doped SnTe [PRB2017], or

(iv) searching for the 3D quantum Hall effect in the semi-metals CaCuSb and CaCu4As2 [PRB2021, PRR(L)2021] in collaboration with Prof. A. Thamizhavel's group in TIFR.

Selected Publications

Publications arranged in reverse chronological order. Click to see the list.

Students and postdocs

Past graduate students

Kusum Dhochak (faculty at IIT Palakkad)

Sarath Sankar (postdoc at Tel Aviv University)

Sarbajaya Kundu (Dirac Postdoctoral Fellow at University of Florida, Gainesville)

Aman Kumar (Dirac Postdoctoral Fellow at National High Magnetic Field Lab, Tallahassee)

Sanjeev Kumar (postdoc at TU Berlin)

Jagannath Das (postdoc at Virginia Tech, Blacksburg)

Current graduate students

Avijit Maity

Ayush Sharma

Past postdoc

Himadri Barman (postdoc at National Taiwan University, Taipei, Taiwan)

Awards and honours

2014-2019: Swarnajayanti Fellowship awarded by Department of Science and Technology, Government of India

2014-15: Award from University of Chicago Center in New Delhi for Sabbatical at Argonne National Laboratory/University of Chicago

2007-2012: Ramanujan Fellowship awarded by Department of Science and Technology, Government of India

2007-2009: Associateship of the Indian Academy of Sciences, Bangalore

2002-06: Elected to Title A Fellowship of Trinity College, University of Cambridge

Professor of Physics
Department of Theoretical Physics