Level statistics of disordered spin-1/2 systems and its implications for materials with localized Cooper pairs

TL;DR

This paper investigates the energy level statistics of disordered spin-1/2 systems, revealing a quantum phase transition between discrete and continuous spectra, with implications for understanding insulating phases in disordered superconductors.

Contribution

It provides the first numerical evidence of a quantum phase transition in energy level statistics of disordered spin systems, linking it to superconductor-insulator transitions.

Findings

Identification of a quantum phase transition between discrete and continuous spectra.

Evidence of novel insulating phases near the superconductor-insulator transition.

Implications for energy level broadening and intrinsic decoherence in large disordered quantum systems.

Abstract

The origin of continuous energy spectra in large disordered interacting quantum systems is one of the key unsolved problems in quantum physics. While small quantum systems with discrete energy levels are noiseless and stay coherent forever in the absence of any coupling to external world, most large-scale quantum systems are able to produce thermal bath and excitation decay. This intrinsic decoherence is manifested by a broadening of energy levels which aquire a finite width. The important question is what is the driving force and the mechanism of transition(s) between two different types of many-body systems - with and without intrinsic decoherence? Here we address this question via the numerical study of energy level statistics of a system of spins-1/2 with anisotropic exchange interactions and random transverse fields. Our results present the first evidence for a well-defined quantum phase transition between domains of discrete and continous many-body spectra in a class of random spin models. Because this model also describes the physics of the superconductor-insulator transition in disordered superconductors like InO and similar materials, our results imply the appearance of novel insulating phases in the vicinity of this transition.