Construction of exact constants of motion and effective models for many-body localized systems

TL;DR

This paper introduces a novel method to precisely identify a complete set of exact, quasi-local conserved quantities in many-body localized systems, advancing understanding of their effective Hamiltonians and transport properties.

Contribution

It develops a new approach for constructing exact constants of motion in many-body localized systems, improving upon approximate numerical methods.

Findings

Constructed a complete set of exact conserved operators.

Enabled investigation of effective Hamiltonians via exact diagonalization.

Provided tools to better understand breakdown of transport in disordered systems.

Abstract

One of the defining features of many-body localization is the presence of extensively many quasi-local conserved quantities. These constants of motion constitute a corner-stone to an intuitive understanding of much of the phenomenology of many-body localized systems arising from effective Hamiltonians. They may be seen as local magnetization operators smeared out by a quasi-local unitary. However, accurately identifying such constants of motion remains a challenging problem. Current numerical constructions often capture the conserved operators only approximately restricting a conclusive understanding of many-body localization. In this work, we use methods from the theory of quantum many-body systems out of equilibrium to establish a new approach for finding a complete set of exact constants of motion which are in addition guaranteed to represent Pauli-$z$ operators. By this we are able to construct and investigate the proposed effective Hamiltonian using exact diagonalization. Hence, our work provides an important tool expected to further boost inquiries into the breakdown of transport due to quenched disorder.