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

Journal Article · 13 February 2022 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.105.085120 · OSTI ID:1879837

Christos, Maine ^[1]; Haehl, Felix M.  ^[2]; Sachdev, Subir  ^[3]

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1. Harvard Univ., Cambridge, MA (United States); Institute for Advanced Study
2. Institute for Advanced Study, Princeton, NJ (United States)
3. Harvard Univ., Cambridge, MA (United States); Institute for Advanced Study, Princeton, NJ (United States)

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. Furthermore, 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.

• Research Organization: Institute for Advanced Study, Princeton, NJ (United States)
• Sponsoring Organization: National Science Foundation; USDOE Office of Science (SC); USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: SC0009988
• OSTI ID: 1879837
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 8 Vol. 105; ISSN 2469-9950
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English