Spectral and Entanglement Properties of the Random Exchange Heisenberg Chain

TL;DR

This paper investigates the spectral and entanglement properties of a 1D non-abelian SU(2)-invariant random antiferromagnetic exchange model, revealing differences from the random field Heisenberg model in localization behavior.

Contribution

It provides the first detailed analysis of spectral and entanglement features in the non-abelian random exchange Heisenberg chain, highlighting distinctions from the field model.

Findings

Less pronounced localization regime compared to the random field Heisenberg model

Distinct spectral and entanglement signatures in the non-abelian model

Behavior varies with different disorder distributions

Abstract

We study the many-body localization problem in the non-abelian SU(2)-invariant random antiferromagnetic exchange model in 1D. Exact and sparse matrix diagonalization methods are used to calculate eigenvalues and eigenvectors of the Hamiltonian matrix. We investigate the behaviour of the energy level gap-ratio statistic, participation ratio, entanglement entropy and the entanglement spectral parameter as a function of disorder strength. Different distributions of random couplings are considered. We find, up to $L=24$, a clear distinction between our non-abelian model and the more often studied random field Heisenberg model: the regime of seemingly localized behaviour is much less pronounced in the random exchange model than in the field model case.