Mean-Field Theory of a Quantum Heisenberg Spin Glass

TL;DR

This paper provides a comprehensive mean field analysis of a quantum Heisenberg spin glass model, revealing a spin glass transition across all spins, quantum critical behavior, and specific heat characteristics, with links to classical dynamics.

Contribution

It introduces a full mean field solution for the quantum Heisenberg spin glass in the large-N limit, exploring phase transitions and critical regimes.

Findings

Spin glass transition occurs for all spin values.

Specific heat vanishes linearly with temperature.

Connections between quantum equilibrium and classical out-of-equilibrium dynamics.

Abstract

A full mean field solution of a quantum Heisenberg spin glass model is presented in a large-N limit. A spin glass transition is found for all values of the spin S. The quantum critical regime associated with the quantum transition at S=0, and the various regimes in the spin glass phase at high spin are analyzed. The specific heat is shown to vanish linearly with temperature. In the spin-glass phase, intriguing connections between the equilibrium properties of the quantum problem and the out-of-equilibrium dynamics of classical models are pointed out.