Equilibrium dynamics of infinite-range quantum spin glasses in a field

• URL: http://arxiv.org/abs/2309.03255v1
• Date: Wed, 6 Sep 2023 18:00:00 GMT
• Title: Equilibrium dynamics of infinite-range quantum spin glasses in a field
• Authors: Maria Tikhanovskaya, Subir Sachdev, Rhine Samajdar
• Abstract summary: We study the symmetry breaking function for the spin glass phase of the quantum Ising model. For all $h, the spin state has full replica symmetry breaking, and gaplessness only appears after imposition of an additional marginal stability condition.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We determine the low-energy spectrum and Parisi replica symmetry breaking function for the spin glass phase of the quantum Ising model with infinite-range random exchange interactions and transverse and longitudinal ($h$) fields. We show that, for all $h$, the spin glass state has full replica symmetry breaking, and the local spin spectrum is gapless with a spectral density which vanishes linearly with frequency. These results are obtained using an action functional$\unicode{x2014}$argued to yield exact results at low frequencies$\unicode{x2014}$that expands in powers of a spin glass order parameter, which is is bilocal in time, and a matrix in replica space. We also present the exact solution of the infinite-range spherical quantum $p$-rotor model at nonzero $h$: here, the spin glass state has one-step replica symmetry breaking, and gaplessness only appears after imposition of an additional marginal stability condition. Possible connections to experiments on random arrays of trapped Rydberg atoms are noted.

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