# Comparing many-body localization lengths via non-perturbative construction of local integrals of motion

## TL;DR

This paper introduces a non-perturbative method to explicitly construct local integrals of motion for many-body localized systems, enabling detailed analysis of localization lengths and system dynamics.

## Contribution

The authors develop a non-perturbative approach to compute complete LIOMs, allowing direct mapping of Hamiltonians and analysis of MBL properties at the microscopic level.

## Key findings

- LIOMs exhibit exponential decay in real space
- Localization lengths can be extracted from LIOM weights
- Method is effective even at phase transition points

## Abstract

Many-body localization (MBL), characterized by the absence of thermalization and the violation of conventional thermodynamics, has elicited much interest both as a fundamental physical phenomenon and for practical applications in quantum information. A phenomenological model, which describes the system using a complete set of local integrals of motion (LIOMs), provides a powerful tool to understand MBL, but can be usually only computed approximately. Here we explicitly compute a complete set of LIOMs with a non-perturbative approach, by maximizing the overlap between LIOMs and physical spin operators in real space. The set of LIOMs satisfies the desired exponential decay of weight of LIOMs in real-space. This LIOM construction enables a direct mapping from the real space Hamiltonian to the phenomenological model and thus enables studying the localized Hamiltonian and the system dynamics. We can thus study and compare the localization lengths extracted from the LIOM weights, their interactions, and dephasing dynamics, revealing interesting aspects of many-body localization. Our scheme is immune to accidental resonances and can be applied even at phase transition point, providing a novel tool to study the microscopic features of the phenomenological model of MBL.