Counting local integrals of motion in disordered spinless-fermion and Hubbard chains

TL;DR

This paper introduces a systematic method to identify and count local integrals of motion in disordered fermionic chains, revealing differences in localization properties between spinless fermions and Hubbard models.

Contribution

The authors develop a new procedure to generate and analyze all conserved operators, distinguishing between full many-body localization and partial localization in disordered fermionic systems.

Findings

Full MBL in spinless fermions with N_M=2^M-1 LIOMs

Hubbard chain shows fewer LIOMs than full MBL, indicating partial localization

Method effectively distinguishes localization regimes in disordered chains

Abstract

We develop a procedure which systematically generates all conserved operators in the disordered models of interacting fermions. Among these operators, we identify and count the independent and local integrals of motion (LIOM) which represent the hallmark of the many-body localization (MBL). The method is tested first on the prototype disordered chain of interacting spinless fermions. As expected for full MBL, we find for large enough disorder $N_M=2^M-1$ independent and quasi-local LIOM with support on $M$ consecutive sites. On the other hand, the study of the disordered Hubbard chain reveals that $3^M-1< N_M < 4^M/2$ which is less than required for full MBL but much more than in the case of spinless fermions.