Explicit Local Integrals of Motion for the Many-Body Localized State

TL;DR

This paper introduces an exact, iterative method to identify local integrals of motion in many-body localized systems, enabling detailed analysis of localization transitions in various models.

Contribution

The authors develop a Hilbert space preserving renormalization scheme using displacement operators to find local integrals of motion exactly, applicable across different dimensions and Hamiltonians.

Findings

Demonstrated localization and delocalization transition in interacting fermion chains

Provided a general scheme for studying many-body localization

Applicable to disorder-free Hamiltonians

Abstract

Recently, it has been suggested that the Many-Body Localized phase can be characterized by local integrals of motion. Here we introduce a Hilbert space preserving renormalization scheme that iteratively finds such integrals of motion exactly. Our method is based on the consecutive action of a similarity transformation using displacement operators. We show, as a proof of principle, localization and the delocalization transition in interacting fermion chains with random onsite potentials. Our scheme of consecutive displacement transformations can be used to study Many Body Localization in any dimension, as well as disorder-free Hamiltonians.