Research

I have been working on several aspects of strongly correlated systems - statics, dynamics, renormalization, computation, connection to experiments etc. A common thread connecting my work is to think about condensed matter problems in the language of quantum many-body wavefunctions and Hilbert space approaches. While the viewpoint is as old as quantum mechanics itself,  some more modern developments allow one to do interesting things with it. I am of the firm belief that progress in this direction requires both analytic and computational thinking.

You can access my PhD thesis here to know more. It is primarily on developing new computational many-body techniques, and applying them to the study of dilution-disordered quantum magnets. Since then I have ventured into other related areas of this field of research, which I briefly describe below. 

Quantum statics and dynamics of magnetic systems

Our modern understanding of "strongly-correlated" quantum systems, based on new theoretical tools and computational techniques, has been central to research on phases of quantum matter beyond the Landau-Ginzburg-Wilson framework. These include topological phases, which were honored by the Nobel Prize for Kosterlitz, Thouless and Haldane in 2016. My focus has been on quantum spin liquids (QSLs), phases of matter that had previously been studied purely for academic interest, but have now shown to be potentially useful for quantum computers.

Such QSLs are most naturally found in systems with several competing classical ground states - among these are "frustrated” magnets where all individual conditions for minimizing the energy of interacting spins can not be simultaneously satisfied due to geometrical constraints. In practice, these phases have eluded the community from being realized, because at the lowest temperatures spins typically relieve frustration by forming a symmetry- broken ordered state. Over the last decade however, several experimental and theoretical studies of materials and models (including our own!) with triangular, kagome,  and pyrochlore geometries have reported the existence of QSLs. Even where the material or model was not found to be a QSL, the associated physics is often rich and interesting. 

We recently realized that everything we have learned or contributed to in the equilibrium context exhibits equally interesting non equilibrium effects i.e. in the time domain. For example, we recently proposed that "quantum scars" and "Hilbert space fragmentation" can be studied in frustrated magnets with very simple Hamiltonians. Some aspects of this work rely on our (somewhat lucky!) finding of ground states at solvable points in a class of models (including the XXZ model with two-spin terms) for magnetic systems. The ground states are "coloring" (coherent) states and, by virtue of the frustration, their number can be exponential. What is interesting is how the Hilbert space organizes itself and what effect this has on quantum relaxation dynamics.


Publications in this area of research  

 Thermodynamics of the dipole-octupole pyrochlore magnet Ce2Hf2O7 in applied magnetic fields, arXiv: 2402.08723 (2024), under review

A recent video can be found here.

A recent representative talk is posted here.

An older representative talk on this subject is posted here

And another one (based on my PhD thesis work) is posted here 

Correlated phases of electronic matter

Recently, I have ventured into areas where not only the spin, but the charge degrees of freedom are also important. One such puzzle is related to the occurrence of "strange metal" ("non Fermi liquid") phase in the phase diagram of the high-temperature superconductors. Recent Moire materials also show the non Fermi liquid phase among other electronic and magnetic phases. There is no "quasiparticle" description of this phase (that we know of) and the description of the dynamics of strongly correlated quantum matter in such situations is a challenge. My take on this longstanding issue (30+ years?) is to think in the language of many-body wavefunctions - they are democratic in a certain sense - they do not care if there are underlying quasiparticles or not. That led us to a careful review of the many-body Kubo formula from linear response theory, involving matrix elements of the current operator computed with many-body wave functions. We derived a simple criterion for the occurrence of T-linear resistivity and identified a many-body energy invariant based on an analysis of the contributions to the many-body Kubo formula. 

Publications in this area of research


*denotes equal contribution

Density matrix downfolding materials to models

Due to advances in computer hardware and new algorithms, it is now possible to perform highly accurate many-body simulations of realistic materials with all their intrinsic complications. The success of these simulations raises some natural questions, for example, how do we extract useful physical models and insight from these simulations? To address this, I have co-developed a many-body version of "downfolding"–extracting an effective Hamiltonian from first-principles calculations. The theory maps the downfolding problem into fitting information derived from wave functions sampled from a low-energy subspace of the full Hilbert space. This fitting process most commonly uses reduced density matrices, we term it density matrix downfolding (DMD).

Publications in this area of research

I have given several talks on the subject, one of them is posted here

Quantum many body algorithms and simulations 

A key advance in the accurate simulation of low dimensional quantum systems for coarse grained lattice models has been the density matrix renormalization group which led to concepts such as matrix product states and tensor network states.  We have been exploring this area in several directions - such as by working with tree tensor networks and by combining Monte Carlo with tensor networks. A neural network is also a type of tensor network with a close connection to correlator product states, which themselves are extended Jastrow or Marshall-Huse-Elser wavefunctions.

Publications in this area of research