Energy-gap analysis of quantum spin-glass transitions at zero temperature

TL;DR

This paper investigates the energy gap behavior in quantum spin-glass models at zero temperature, revealing that gap vanishing does not always indicate phase transitions and highlighting the role of quantum Griffiths effects.

Contribution

It provides a detailed analysis of the energy gap in quantum spin-glass systems, showing the limitations of gap vanishing as a transition indicator and identifying quantum Griffiths phenomena.

Findings

Vanishing average gap does not mark the phase transition in the transverse SK model.

Power-law gap distributions lead to diverging susceptibilities at different points.

Classical treatment is valid for the transverse REM, with phase transitions indicated by ground state changes.

Abstract

We study for random quantum spin systems the energy gap between the ground and first excited states to clarify a relation to the spin-glass-paramagnetic phase transition. We find that for the transverse Sherrington-Kirkpatrick model the vanishing of the averaged gap does not identify the transition. A power-law form of the gap distribution function leads to power-law distributions of the linear, spin-glass, and nonlinear susceptibilities. They diverge at different points, which we attribute to a quantum Griffiths mechanism. On the other hand, the classical treatment is justified for the transverse random energy model and the phase transition can be found by a sudden change of the ground state.