Spectral Crossovers and Universality in Quantum Spin-chains Coupled to Random Fields

TL;DR

This paper investigates the spectral properties and crossovers in quantum spin-chains with random fields, demonstrating universal behavior in spectral statistics and connecting RMT crossover parameters to physical system parameters.

Contribution

It introduces a detailed analysis of spectral crossovers in spin-chains with random fields, revealing universality and linking RMT parameters to physical variables.

Findings

Spectral crossovers follow universal patterns independent of system size.

RMT crossover parameter correlates with physical parameters via a scaling exponent.

Poissonian to GOE and GOE to GUE transitions are well described by RMT fits.

Abstract

We study the spectral properties of and spectral-crossovers between different random matrix ensembles (Poissonian, GOE, GUE) in correlated spin-chain systems, in the presence of random magnetic fields, and the scalar spin-chirality term, competing with the usual isotropic and time-reversal invariant Heisenberg term. We have investigated these crossovers in the context of the level-spacing distribution and the level-spacing ratio distribution. We use random matrix theory (RMT) analytical results to fit the observed Poissonian-to-GOE and GOE-to-GUE crossovers, and examine the relationship between the RMT crossover parameter {\lambda} and scaled physical parameters of the spin-chain systems in terms of a scaling exponent. We find that the crossover behavior exhibits universality, in the sense that it becomes independent of lattice size in the large Hamiltonian matrix dimension limit.