Spin liquid to spin glass crossover in the random quantum Heisenberg magnet
Spin liquid to spin glass crossover in the random quantum Heisenberg magnet
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.
cond-mat.str-el, cond-mat.dis-nn, hep-th
Christos, Maine
b65c0b30-6232-49d0-8beb-65598e597555
Haehl, Felix M.
eb0d74fd-0d8b-4b1b-8686-79d43c2a3a5f
Sachdev, Subir
60a3d82c-2a68-49a7-b047-4795beb27e03
30 September 2021
Christos, Maine
b65c0b30-6232-49d0-8beb-65598e597555
Haehl, Felix M.
eb0d74fd-0d8b-4b1b-8686-79d43c2a3a5f
Sachdev, Subir
60a3d82c-2a68-49a7-b047-4795beb27e03
[Unknown type: UNSPECIFIED]
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.
Text
2110.00007v1
- Accepted Manuscript
More information
Published date: 30 September 2021
Additional Information:
26 pages, 5 figures
Keywords:
cond-mat.str-el, cond-mat.dis-nn, hep-th
Identifiers
Local EPrints ID: 470065
URI: http://eprints.soton.ac.uk/id/eprint/470065
ISSN: 2331-8422
PURE UUID: c72f69ff-0077-4277-816c-c4c4ce6c2f7e
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Date deposited: 03 Oct 2022 16:31
Last modified: 17 Mar 2024 04:14
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Contributors
Author:
Maine Christos
Author:
Felix M. Haehl
Author:
Subir Sachdev
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