Many-body Localization
Title: Many-body Localization
SNIC Project: SNIC 2022/5-130
Project Type: SNIC Medium Compute
Principal Investigator: Jens Bardarson <bardarson@kth.se>
Affiliation: Kungliga Tekniska högskolan
Duration: 2022-03-29 – 2023-04-01
Classification: 10304
Homepage: https://github.com/DavidAce/DMRG
Keywords:

Abstract

Introducing disorder in interacting quantum systems might break ergodicity and thermalization, a phenomenon known as Many-Body Localization (MBL). Systems exhibiting MBL have gathered increasing interest in the last decade as the dynamics generated by the corresponding Hamiltonian does not follow the Eigenstate Thermalization Hypothesis. As such, the full system fails to act as a thermal bath for its subsystems so that no quantum statistical thermalization appears. Yet, to date, several fundamental questions, mainly regarding the stability of MBL in large or open systems, remain unanswered. Diagnostics of MBL can typically be obtained using Exact Diagonalization (ED) techniques. However, in view of the above problem formulation, ED might not suffice. That is why in this project, we choose a different, two-fold approach: (i) On the one hand, we aim to apply a Density Matrix Renormalization Group (DMRG) study, a numerical technique that uses tensor network formalism to describe many-body quantum states efficiently by keeping only the relevant entanglement information. Naturally, this is most accurate when describing low-entanglement states and therefore well suited to study ground states of Hamiltonians as well as MBL eigenstates. Using DMRG we plan to investigate the self-dual quantum Ising model, describing a disordered one-dimensional spin-lattice system. It has been observed that, depending on disorder strength, the highly excited eigenstates of this model can exhibit either an ergodic phase, a “paramagnetic” MBL phase, or a “spin-glass” MBL phase. Our aim is to clarify the nature of the phase transition between the two MBL regimes. This transition has eluded a full understanding due to the rapid growth of entanglement near the critical region, which poses a formidable computational challenge. (ii) On the other hand, we wish to apply a Diagrammatic Monte Carlo investigation. This numerical method, based on a Markov Chain Monte Carlo sampling in the space of Feynman diagrams, calculates correlation functions in strongly interacting many-body systems. This method is well suited to study the formation and breakdown of MBL in large and/or open systems, where otherwise the effects of interaction and/or external bath can only be incorporated perturbatively. In particular, we aim at investigating the presence of MBL in phonon-coupled disordered spin systems, where a phonon thermal bath can serve as a mediator of spin-spin interactions leading to an MBL regime in the dynamics of the system.