Quantum criticality of hot random spin chains

TL;DR

This paper investigates the infinite-temperature behavior of random quantum spin chains, revealing non-ergodic, quantum critical phases called "quantum critical glasses" with unique entanglement properties and non-equilibrium criticality.

Contribution

It introduces a real-space renormalization group analysis of SU(2)$_k$ anyon chains, uncovering novel non-equilibrium critical phases at high energy levels.

Findings

Identification of non-ergodic behavior at strong disorder

Discovery of quantum critical glasses with critical entanglement scaling

Distinct excited-state fixed points from ground states

Abstract

We study the infinite-temperature properties of an infinite sequence of random quantum spin chains using a real-space renormalization group approach, and demonstrate that they exhibit non-ergodic behavior at strong disorder. The analysis is conveniently implemented in terms of SU(2)$_k$ anyon chains that include the Ising and Potts chains as notable examples. Highly excited eigenstates of these systems exhibit properties usually associated with quantum critical ground states, leading us to dub them "quantum critical glasses". We argue that random-bond Heisenberg chains self-thermalize and that the excited-state entanglement crosses over from volume-law to logarithmic scaling at a length scale that diverges in the Heisenberg limit $k\rightarrow\infty$. The excited state fixed points are generically distinct from their ground state counterparts, and represent novel non-equilibrium critical phases of matter.