Modelling sample-to-sample fluctuations of the gap ratio in finite disordered spin chains

TL;DR

This paper investigates the fluctuations of the gap ratio in disordered spin chains, demonstrating that an extended Rosenzweig-Porter model accurately captures these fluctuations across different regimes, and proposes methods to reduce them.

Contribution

The study introduces an extension to the Rosenzweig-Porter model that accurately reproduces sample-to-sample fluctuations in disordered spin chains across all regimes.

Findings

Fluctuations are well captured by the RP model away from the crossover.

Microscopic models show larger fluctuations near the crossover.

Extended RP model matches fluctuations in all regimes.

Abstract

We study sample-to-sample fluctuations of the gap ratio in the energy spectra in finite disordered spin chains. The chains are described by the random-field Ising model and the Heisenberg model. We show that away from the ergodic/nonergodic crossover, the fluctuations are correctly captured by the Rosenzweig-Porter (RP) model. However, fluctuations in the microscopic models significantly exceed those in the RP model in the vicinity of the crossover. We show that upon introducing an extension to the RP model, one correctly reproduces the fluctuations in all regimes, i.e., in the ergodic and nonergodic regimes as well as at the crossover between them. Finally, we demonstrate how to reduce the sample-to-sample fluctuations in both studied microscopic models.