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Journal Club for Condensed Matter Physics

A New Proof of Many-Body Localization in Finite Spin Chains

Chris R. Laumann

Published Sep 30, 2024• 0 citations
Publisher

Abstract

Absence of Normal Heat Conduction in Strongly Disordered Interacting Quantum Chains Authors: Wojciech De Roeck, Lydia Giacomin, Francois Huveneers, and Oskar Prośniak arXiv:2408.04338, DOI: 10.48550/arXiv.2408.04338 Recommended with a commentary by Chris R. Laumann , Boston University and Max-Planck-Institute for Physics of Complex Systems |View Commentary (pdf)| This commentary may be cited as: DOI: 10.36471/JCCM_September_2024_02 https://doi.org/10.36471/JCCM_September_2024_02

DOI
10.36471/jccm_september_2024_02

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Absence of Normal Heat Conduction in Strongly Disordered Interacting Quantum Chains Authors: Wojciech De Roeck, Lydia Giacomin, Francois Huveneers, and Oskar Prośniak arXiv:2408.04338, DOI: 10.48550/arXiv.2408.04338 Recommended with a commentary by Chris R. Laumann , Boston University and Max-Planck-Institute for Physics of Complex Systems |View Commentary (pdf)| This commentary may be cited as: DOI: 10.36471/JCCM_September_2024_02 https://doi.org/10.36471/JCCM_September_2024_02
The study of disordered systems in statistical mechanics is a topic that garners strong interest from the mathematical and physics communities. In this dissertation, we present two problems dealing with some type of strongly disordered interacting particle system. In particular, we study properties related to transport of energy in these systems. The first model deals with the spreading of wave packets in a 1D lattice governed by the disordered discrete non-linear Schrödinger (DNLS) equation. We study the rate of decay of the maximum of a wave packet initially supported around the origin, and prove slower than power law spreading. The second model deals with many-body localization (MBL), a phenomenon in which certain strongly disordered interacting particle systems fail to reach thermal equilibrium. We prove the vanishing of the heat conductivity for a robust 1D spin chain model. This result serves to constitute a first step toward a rigorous proof of many-body localization.
We reinvestigate the behavior of the conductivity of several disordered quantum lattice models at infinite temperature using exact diagonalization. Contrary to the conclusion drawn in a recent investigation of similar quantities in identical systems, we find evidence of a localized regime for strong random fields. We estimate the location of the critical field for the many-body localization transition for the random-field XXZXXZXXZ spin chain, and compare our findings with recent investigations in related systems.
Many-body localization (MBL) hinders the thermalization of quantum many-body systems in the presence of strong disorder. In this Letter, we study the MBL regime in bond-disordered spin-1/2 XXZ spin chain, finding the multimodal distribution of entanglement entropy in eigenstates, sub-Poissonian level statistics, and revealing a relation between operators and initial states required for examining the breakdown of thermalization in the time evolution of the system. We employ a real space renormalization group scheme to identify these phenomenological features of the MBL regime that extend beyond the standard picture of local integrals of motion relevant for systems with disorder coupled to on-site operators. Our results pave the way for experimental probing of MBL in bond-disordered spin chains.