Behavior of l-bits near the many-body localization transition

TL;DR

This paper develops a non-perturbative method to construct l-bit operators in many-body localized systems, enabling detailed analysis of their algebra, localization lengths, and the transition to thermalization.

Contribution

It introduces a novel algorithm combining exact diagonalization and tensor networks to construct the full set of l-bit algebras in MBL systems.

Findings

Distribution of l-bit localization lengths characterized

Algorithm successfully constructs l-bit algebra in large systems

Localization length distribution used to analyze MBL transition

Abstract

Eigenstates of fully many-body localized (FMBL) systems are described by quasilocal operators $\tau_i^z$ (l-bits), which are conserved exactly under Hamiltonian time evolution. The algebra of the operators $\tau_i^z$ and $\tau_i^x$ associated with l-bits ($\boldsymbol{\tau}_i$) completely defines the eigenstates and the matrix elements of local operators between eigenstates at all energies. We develop a non-perturbative construction of the full set of l-bit algebras in the many-body localized phase for the canonical model of MBL. Our algorithm to construct the Pauli-algebra of l-bits combines exact diagonalization and a tensor network algorithm developed for efficient diagonalization of large FMBL Hamiltonians. The distribution of localization lengths of the l-bits is evaluated in the MBL phase and used to characterize the MBL-to-thermal transition.