Spin liquid to spin glass crossover in the random quantum Heisenberg magnet
Maine Christos, Felix M. Haehl, Subir Sachdev
Abstract
We study quantum SU($M$) spins with all-to-all and random Heisenberg exchange interactions of root-mean-square strength $J$. The $M\ensuremath{\rightarrow}\ensuremath{\infty}$ model has a quantum 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 ${\ensuremath{\omega}}_{*}\ensuremath{\sim}J{q}_{EA}$, and for $\ensuremath{\omega}<{\ensuremath{\omega}}_{*}$, the spin spectral density is linear in $\ensuremath{\omega}$, thus quenching the extensive zero temperature entropy of the spin liquid. The linear $\ensuremath{\omega}$ 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 $T\ensuremath{\rightarrow}0$ to an extensive complexity of the spin glass state. We comment on holographic connections of the confinement transition to the fragmentation of black holes with ${\mathrm{AdS}}_{2}$ horizons.