Gauge Theory for Quantum Spin Glasses

TL;DR

This paper extends gauge theory to quantum spin glasses, deriving exact results and inequalities, and analyzing phase diagrams and order properties in various quantum spin models.

Contribution

It introduces a quantum gauge theory framework for spin glasses, proving gauge invariance and establishing new inequalities and phase diagram results.

Findings

Gauge invariance in quantum models like the transverse Ising and gauge glass.

An identity relating gauge invariant operator expectations in different limits.

No long-range order in the 2D quantum gauge glass ground state.

Abstract

The gauge theory for random spin systems is extended to quantum spin glasses to derive a number of exact and/or rigorous results. The transverse Ising model and the quantum gauge glass are shown to be gauge invariant. For these models, an identity is proved that the expectation value of the gauge invariant operator in the ferromagnetic limit is equal to the one in the classical equilibrium state on the Nishimori line. As a result, a set of inequalities for the correlation function are proved, which restrict the location of the ordered phase. It is also proved that there is no long-range order in the two-dimensional quantum gauge glass in the ground state. The phase diagram for the quantum XY Mattis model is determined.