Exploring one particle orbitals in large Many-Body Localized systems

TL;DR

This paper investigates the properties of one particle orbitals in large many-body localized systems, revealing their behavior across the MBL transition and their relation to eigenstate energies using advanced numerical methods.

Contribution

It introduces the use of shift-and-invert MPS to analyze one particle orbitals in large MBL systems, providing new insights into their structure and correlations.

Findings

High overlap of orbitals across different energy densities

Maximal standard deviation of IPR at the mobility edge

Exponential decay of orbitals with increasing correlation length at low disorder

Abstract

Strong disorder in interacting quantum systems can give rise to the phenomenon of Many-Body Localization (MBL), which defies thermalization due to the formation of an extensive number of quasi local integrals of motion. The one particle operator content of these integrals of motion is related to the one particle orbitals of the one particle density matrix and shows a strong signature across the MBL transition as recently pointed out by Bera et al. [Phys. Rev. Lett. 115, 046603 (2015); Ann. Phys. 529, 1600356 (2017)]. We study the properties of the one particle orbitals of many-body eigenstates of an MBL system in one dimension. Using shift-and-invert MPS (SIMPS), a matrix product state method to target highly excited many-body eigenstates introduced in [Phys. Rev. Lett. 118, 017201 (2017)], we are able to obtain accurate results for large systems of sizes up to L = 64. We find that the one particle orbitals drawn from eigenstates at different energy densities have high overlap and their occupations are correlated with the energy of the eigenstates. Moreover, the standard deviation of the inverse participation ratio of these orbitals is maximal at the nose of the mobility edge. Also, the one particle orbitals decay exponentially in real space, with a correlation length that increases at low disorder. In addition, we find a 1/f distribution of the coupling constants of a certain range of the number operators of the OPOs, which is related to their exponential decay.