Many-body localization as a large family of localized ground states

TL;DR

This paper demonstrates that ground-state methods can effectively approximate high-energy many-body localized states in disordered quantum systems, simplifying the study of MBL phenomena.

Contribution

It introduces a novel approach to study high-energy MBL states using ground-state algorithms, leveraging covariance matrix computations and DMRG techniques.

Findings

Localized ground states closely approximate high-energy eigenstates.

Effective use of DMRG for large disordered systems up to 256 sites.

High-energy MBL physics can be explored via ground-state methods.

Abstract

Many-body localization (MBL) addresses the absence of thermalization in interacting quantum systems, with non-ergodic high-energy eigenstates behaving as ground states, only area-law entangled. However, computing highly excited many-body eigenstates using exact methods is very challenging. Instead, we show that one can address high-energy MBL physics using ground-state methods, which are much more amenable to many efficient algorithms. We find that a localized many-body ground state of a given interacting disordered Hamiltonian $\mathcal{H}_0$ is a very good approximation for a high-energy eigenstate of a parent Hamiltonian, close to $\mathcal{H}_0$ but more disordered. This construction relies on computing the covariance matrix, easily achieved using density-matrix renormalization group for disordered Heisenberg chains up to $L=256$ sites.