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

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.

49 pages, 13 figures

References in corpus (3)

• Stability of the quantum Sherrington-Kirkpatrick spin glass model
• Quantum fluctuations in the transverse Ising spin glass model: A field theory of random quantum spin systems
• Dynamical Mean-Field Theory and Aging Dynamics

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• A multimode cavity QED Ising spin glass
• Spin-glass quantum phase transition in amorphous arrays of Rydberg atoms
• Energy gap of quantum spin glasses: a projection quantum Monte Carlo study