Emergence of superconductivity from a non-Fermi liquid ground state is seen in many strongly-correlated systems. However a precise description is not well understood since it is not described by the standard BCS theory of superconductivity. Using a solvable model of non-Fermi liquid in the SYK class we systematically studied the SC emerging from a NFL in contrast to that from a FL. We find an enhancement of SC transition temperature in the NFL case. Compared to the FL case, the electron spectral function in the SC phase emerging from NFL is very different and has additional peaks at higher energies, which may be viable fingerprints. Also, the usual Hebel-Slichter peak in the NMR-relaxation disappears in the NFL case. 

Phys. Rev. Research 5, 013045 (2023)

The overdoped phase of cuprates is often assumed to be a conventional Fermi liquid. However, recent experiments indicate that the strange-metal phase extends over a wide range of dopings. We show that a model of electrons with random exchange interaction, where the electron fractionalizes into spinon and holon, hosts a non-Fermi liquid phase in a wide doping range. The features of this phase are in accord with experiments, including a linear-in-temperature contribution to resistivity. Moreover, the spin-correlator exponent has a doping dependent value. At low dopings the non-Fermi liquid phase has an instability to a spin-glass phase, which is also observed in experiments on certain cuprates.

Proceedings of the National Academy of Sciences 119, e2206921119 (2022)

We investigate the t-J model with all sites connected to each other with random hopping, t, and random spin exchange, J. We find a deconfined quantum critical point at finite doping where we show exactly to all orders in perturbation that the spin correlation decays as 1/τ, with τ  being the imaginary time. This is exactly the behavior found in the SYK model. This model might be relevant to underdoped cuprates.

Phys. Rev. X 10, 021033 (2020)

The topological aspects, widely discussed in the fermionic systems, need not be restricted to the ground state of electrons. The excitation spectrum in certain frustrated quantum magnets could be topological in nature. The Kitaev-Heisenberg model is a cornerstone in the study of quantum spin-liquid candidate materials like Na2IrO3 and RuCl3. In this work, we present an interesting and surprising result that the quasiparticles in the ferromagnetic Kitaev-Heisenberg model have a non-trivial Berry curvature leading to a non-zero Chern-number topological invariant. Consequently, there are chiral edge excitations along the zig-zag edge, which can be detected in scattering and thermal- or spin-transport experiments. 

Phys. Rev. B (Rapid Commn.) 98, 060405 (2018) [Editor's suggestion]

Many frustrated magnets host exotic states of matter with non-trivial ground states. We show that in certain systems even if the ground state is trivial (quantum paramagnet), one can realize exotic states by the virtue of non-trivial topological excitations. We call such systems topological quantum paramagnets. These topological excitations are in a way analogs of the fermionic topological states of matter, albeit with many differences. We show that the paramagnetic phase of coupled-dimer systems on a ladder as well as a honeycomb bilayer support topological excitations in the presence of spin-orbit coupling. These excitations are localized at the edges and in case of the ladder they are even fractionalized. We discuss relevant observables, topological invariants, and possible experimental signatures.

Phys. Rev. B (Rapid Commn.) 96, 220405 (2017), 

Phys. Rev. B (Rapid Commn.) 100, 020407 (2019)

In the study of various strongly interacting condensed-matter systems controlled microscopic theories hold a key position. Spin-wave theory, large-N expansion and ε-expansion are some of the few successful cornerstones. In my doctoral thesis work I have developed a large-d expansion (d is spatial dimension) method to study magnetic quantum phase transition between a quantum paramagnet and a magnetically ordered phase. A highlight of this technique is that it can consistently describe the entire phase diagram for the above mentioned case. The idea of large-d formalism is that in the limit of infinite d non-local fluctuations are suppressed, such that observables can be calculated order by order in 1/d by expanding around a suitable product state. I have demonstrated this method in two important systems namely coupled-dimer magnets and the transverse field Ising model. Comparison with quantum Monte Carlo study in d=2 and d=3 yields a very good agreement. Another success of this work is in describing the amplitude (Higgs) mode in this system. 

Phys. Rev. B 91, 094404 (2015), Phys. Rev. B 91, 094405 (2015)

Quantum Hertz entropy (analogue of classical volume entropy) was previously shown to increase (or stay constant) upon driving an isolated quantum system with non-degenerate spectrum out of equilibrium. However in case of isolated systems with degenerate spectrum there is no known analytic proof for the adherence to Clausius principle. So it was important to verify the validity of quantum Hertz entropy in such systems. A system of spin-1/2 XY chain serves as a simple non-trivial situation where the spectrum has degeneracy. In this project two quantum spin-1/2 XY chains at different temperatures were quenched and the resulting change in quantum Hertz entropy was shown to be positive (consistent with the second law of thermodynamics). Moreover, thermalization after the quench was studied and the nearest equilibrium state was quantified using the `Hilbert-Schmidt' distance. The outcome is that the quenched system is not very far from equilibrium and one can associate a temperature corresponding to it.

Eur. Phys. J. B 86, 157 (2013)