Gauge Theory for Quantum Spin Glasses

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.

15 pages, 2 figures

References in corpus (3)

• Numerical Study of a Superconducting Glass Model
• Phase Transition in the Two-Dimensional Gauge Glass
• Dynamical Gauge Theory for the XY Gauge Glass Model

Cited by in corpus (9)

• Continuous symmetry breaking along the Nishimori line
• Nonequilibrium work on spin glasses in longitudinal and transverse fields
• Nonequilibrium work performed in quantum annealing
• Boundedness of Susceptibility in Spin Glass Transition of Transverse Field Mixed $p$-spin Glass Models
• Gauge theory for mixed $p$-spin glasses
• The planted XY model: thermodynamics and inference
• A simple relation between frustration and transition points in diluted spin glasses
• Toward mean-field bound for critical temperature on Nishimori line
• Gauge theory for quantum XYZ spin glasses