Low-energy fixed points of random Heisenberg models

TL;DR

This paper investigates the low-energy fixed points of disordered Heisenberg models in two and three dimensions, revealing universal behaviors and differences between frustrated and non-frustrated systems through numerical renormalization group analysis.

Contribution

It identifies two universal fixed points in disordered Heisenberg models and characterizes their low-energy and dynamical properties, contrasting with one-dimensional behaviors.

Findings

Fixed points with disorder-independent gap exponents

Different fixed points for frustrated and non-frustrated models

No infinite randomness behavior in higher dimensions

Abstract

The effect of quenched disorder on the low-energy and low-temperature properties of various two- and three-dimensional Heisenberg models is studied by a numerical strong disorder renormalization group method. For strong enough disorder we have identified two relevant fixed points, in which the gap exponent, omega, describing the low-energy tail of the gap distribution, P(Delta) ~ Delta^omega is independent of disorder, the strength of couplings and the value of the spin. The dynamical behavior of non-frustrated random antiferromagnetic models is controlled by a singlet-like fixed point, whereas for frustrated models the fixed point corresponds to a large spin formation and the gap exponent is given by omega ~ 0. Another type of universality classes is observed at quantum critical points and in dimerized phases but no infinite randomness behavior is found, in contrast to one-dimensional models.