Highly-symmetric random one-dimensional spin models

TL;DR

This paper develops a strong-disorder renormalization group method for one-dimensional spin models with continuous symmetries, revealing emergent SU(N) symmetry and distinct phases in disordered magnetic chains.

Contribution

It introduces a versatile SDRG scheme applicable to Lie-algebra valued Hamiltonians, enabling analysis of symmetry emergence and phase structure in disordered spin chains.

Findings

Existence of different randomness-dominated phases in SO(N) and Sp(N) chains

Emergent SU(N) symmetry at low energies

Identification of meson-like and baryon-like phases

Abstract

The interplay of disorder and interactions is a challenging topic of condensed matter physics, where correlations are crucial and exotic phases develop. In one spatial dimension, a particularly successful method to analyze such problems is the strong-disorder renormalization group (SDRG). This method, which is asymptotically exact in the limit of large disorder, has been successfully employed in the study of several phases of random magnetic chains. Here we develop an SDRG scheme capable to provide in-depth information on a large class of strongly disordered one-dimensional magnetic chains with a global invariance under a generic continuous group. Our methodology can be applied to any Lie-algebra valued spin Hamiltonian, in any representation. As examples, we focus on the physically relevant cases of SO(N) and Sp(N) magnetism, showing the existence of different randomness-dominated phases. These phases display emergent SU(N) symmetry at low energies and fall in two distinct classes, with meson-like or baryon-like characteristics. Our methodology is here explained in detail and helps to shed light on a general mechanism for symmetry emergence in disordered systems.