The Low-Energy Fixed Points of Random Quantum Spin Chains

TL;DR

This paper studies disordered quantum spin chains, revealing a universality class characterized by large effective spins and specific low-temperature behaviors, with fixed points influenced by initial disorder distributions.

Contribution

It introduces a real-space renormalization group analysis showing a universality class with large spins and fixed points with non-universal exponents in disordered quantum spin chains.

Findings

Systems exhibit a large-spin phase with diverging magnetic susceptibility.

The specific heat vanishes as T^delta |ln T| with delta approximately 0.44.

Fixed-point distributions depend on initial disorder, indicating a line of fixed points.

Abstract

The one-dimensional isotropic quantum Heisenberg spin systems with random couplings and random spin sizes are investigated using a real-space renormalization group scheme. It is demonstrated that these systems belong to a universality class of disordered spin systems, characterized by weakly coupled large effective spins. In this large-spin phase the uniform magnetic susceptibility diverges as 1/T with a non-universal Curie constant at low temperatures T, while the specific heat vanishes as T^delta |ln T| for T->0. For broad range of initial distributions of couplings and spin sizes the distribution functions approach a single fixed-point form, where delta \approx 0.44. For some singular initial distributions, however, fixed-point distributions have non-universal values of delta, suggesting that there is a line of fixed points.