Mean-Field Theory of a Quantum Heisenberg Spin Glass

TL;DR

A full mean-field solution of a quantum Heisenberg spin-glass model is presented in a large- N limit and intriguing connections between the equilibrium properties of the quantum problem and the out-of-equilibrium dynamics of classical models are pointed out.

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.

Figures (3)

• Figure 1: Mean-field phase diagram and crossovers of the large-$N$ quantum Heisenberg spin glass (the various regimes are discussed in the text).
• Figure 2: Relaxation function $\chi"(\omega)/\omega$ in the large-$S$ limit, obtained from (\ref{['EqQuartic']}).
• Figure 3: Specific heat $C (T)$ and internal energy $U (T)$ (inset) vs. temperature $T$, from a numerical solution of Eqs. (\ref{['EqSG']}-\ref{['EqSG_x']}) for $S=5$.