Explicit construction of local conserved operators in disordered many-body systems

TL;DR

This paper explicitly constructs local conserved operators in disordered 1D spin chains, demonstrating their exponential decay in the many-body localized phase and their algebraic properties, providing insights into quantum dynamics and localization.

Contribution

The work introduces a direct minimization method to construct local integrals of motion in disordered spin chains, confirming their exponential decay and algebraic structure in the MBL phase.

Findings

Existence of a large set of local integrals of motion in MBL phase

Operators decay exponentially in the localized phase

Operators are well-described by dressed spin operators

Abstract

The presence and character of local integrals of motion -- quasi-local operators that commute with the Hamiltonian -- encode valuable information about the dynamics of a quantum system. In particular, strongly disordered many-body systems can generically avoid thermalisation when there are extensively many such operators. In this work, we explicitly construct local conserved operators in $1$D spin chains by directly minimising their commutator with the Hamiltonian. We demonstrate the existence of an extensively large set of local integrals of motion in the many-body localised phase of the disordered XXZ spin chain. These operators are shown to have exponentially decaying tails, in contrast to the ergodic phase where the decay is (at best) polynomial in the size of the subsystem. We study the algebraic properties of localised operators, and confirm that in the many-body localised phase they are well-described by "dressed" spin operators.