Landau theory of quantum spin glasses of rotors and Ising spins

TL;DR

This paper develops a Landau theory for quantum spin glasses of rotors and Ising spins, analyzing their phase transitions, critical behavior, and fluctuations in finite dimensions, extending earlier infinite-range models.

Contribution

It introduces a Landau effective-action functional for finite-dimensional quantum spin glasses and explores their phase diagram and critical properties, including fluctuation effects and renormalization group analysis.

Findings

Mean-field phase diagram mapped out near zero temperature.

Spin glass ground state is replica symmetric, with symmetry breaking at finite temperatures.

Transition controlled by Gaussian fixed point above dimension 8, with strong coupling flows below.

Abstract

We consider quantum rotors or Ising spins in a transverse field on a $d$-dimensional lattice, with random, frustrating, short-range, exchange interactions. The quantum dynamics are associated with a finite moment of inertia for the rotors, and with the transverse field for the Ising spins. For a suitable distribution of exchange constants, these models display spin glass and quantum paramagnet phases and a zero temperature quantum transition between them. An earlier exact solution for the critical properties of a model with infinite-range interactions can be reproduced by minimization of a Landau effective-action functional for the model in finite $d$ with short-range interactions. The functional is expressed in terms of a composite spin field which is bilocal in time. The mean-field phase diagram near the zero temperature critical point is mapped out as a function of temperature, strength of the quantum coupling, and applied fields. The spin glass ground state is found to be replica symmetric, with replica symmetry breaking appearing only at finite temperatures. Next we examine the consequences of fluctuations about mean-field for the critical properties. Above $d=8$, and with certain restrictions on the values of the Landau couplings, we find that the transition is controlled by a Gaussian fixed point with mean-field critical exponents. For couplings not attracted by the Gaussian fixed point above $d=8$, and for all physical couplings below $d=8$, we find runaway renormalization group flows to strong coupling. General scaling relations that should be valid even at the strong coupling fixed point are proposed and compared with Monte Carlo simulations.