Spin liquid to spin glass crossover in the random quantum Heisenberg magnet

TL;DR

This paper investigates the crossover from a quantum spin liquid to a spin glass in a random SU(M) Heisenberg model, revealing how SYK-like behavior persists at intermediate frequencies and transitions to spin glass order at low frequencies.

Contribution

It introduces a $1/M$ expansion to describe the transition from a SYK spin liquid to a spin glass, connecting the extensive entropy of the spin liquid to the complexity of the glass state.

Findings

SYK spin liquid behavior persists down to a frequency $\\omega_*$.

Spectral density becomes linear in $\omega$ below $\omega_*$.

Extensive entropy of the spin liquid transforms into spin glass complexity.

Abstract

We study quantum SU($M$) spins with all-to-all and random Heisenberg exchange interactions of root-mean-square strength $J$. The $M \rightarrow \infty$ model has a spin liquid ground state with the spinons obeying the equations of the Sachdev-Ye-Kitaev (SYK) model. Numerical studies of the SU(2) model with $S=1/2$ spins show spin glass order in the ground state, but also display SYK spin liquid behavior in the intermediate frequency spin spectrum. We employ a $1/M$ expansion to describe the crossover from fractionalized fermionic spinons to a confining spin glass state with weak spin glass order $q_{EA}$. The SYK spin liquid behavior persists down to a frequency $\omega_\ast \sim J q_{EA}$, and for $\omega < \omega_\ast$, the spectral density is linear in $\omega$, thus quenching the extensive zero temperature entropy of the spin liquid. The linear $\omega$ spectrum is qualitatively similar to that obtained earlier using bosonic spinons for large $q_{EA}$. We argue that the extensive SYK spin liquid entropy is transformed as $T \rightarrow 0$ to an extensive complexity of the spin glass state.