Multibody expansion of the local integrals of motion: How many pairs of particle-hole do we really need to describe the quasiparticles in the many-body localized phase?

TL;DR

This paper investigates how many particle-hole pairs are necessary to accurately describe quasiparticles in the many-body localized phase, revealing that higher-order corrections can lead to a breakdown of the single-particle picture.

Contribution

The authors explicitly derive the multibody expansion of LIOM creation operators in a disordered XXZ chain, quantifying the impact of higher-order particle-hole excitations.

Findings

Higher-order particle-hole contributions can significantly alter the quasiparticle description.

The effective one-particle picture breaks down depending on the localization length.

The multibody expansion coefficients are analytically obtained and analyzed.

Abstract

The emergent integrability in a many-body localized (MBL) system can be well characterized by the existence of the complete set of local integrals of motion (LIOMs). Such exactly conserved and exponentially localized operators are often understood as quasiparticle operators which can be expanded in terms of single-particle operators dressed with different numbers of particle-hole pairs. Here, we consider a one-dimensional XXZ spin-$\frac12$ Heisenberg chain in the presence of a random field and try to quantify the corrections needed to be considered in the picture of quasiparticles associated with LIOMs due to the presence of particle-hole excitations. To this end, we explicitly present the multibody expansion of LIOM creation operators of the system in the MBL regime. We analytically obtain the coefficients of this expansion and discuss the effect of higher-order corrections associated with different numbers of particle-hole excitations. Our analysis shows that depending on the localization length of the system, there exist a regime in which the contributions that come from higher-order terms can break down the effective one-particle description of the LIOMs and such quasiparticles become essentially many-body-like.