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.

arXiv comment49 pages, 13 figures

References in corpus (40)

• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Adiabatic Quantum Computing
• Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model
• On the Out of Equilibrium Relaxation of the Sherrington - Kirkpatrick model
• Spin-Glass Theory for Pedestrians
• Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays
• Quantum critical dynamics in a 5000-qubit programmable spin glass
• Non-Fermi liquid regime of a doped Mott insulator
• Quantum Fluctuations of a Nearly Critical Heisenberg Spin Glass
• Measuring equilibrium properties in aging systems
• Mean-Field Theory of a Quantum Heisenberg Spin Glass
• Landau theory of quantum spin glasses of rotors and Ising spins
• A Solvable Spin-Glass of Quantum Rotors
• Quantum optimization with arbitrary connectivity using Rydberg atom arrays
• Real-time non-equilibrium dynamics of quantum glassy systems
• The Quantum Spherical p-Spin-Glass Model
• Quantum TAP equations
• Quantum simulation of Ising spins on Platonic graphs
• Quenched complexity of the p-spin spherical spin-glass with external magnetic field
• Dynamics of the Ising Spin-Glass Model in a Transverse Field
• The Quantum Approximate Optimization Algorithm at High Depth for MaxCut on Large-Girth Regular Graphs and the Sherrington-Kirkpatrick Model
• Aging dynamics of quantum spin glasses of rotors
• Out of equilibrium dynamics of a Quantum Heisenberg Spin Glass
• Stability of the quantum Sherrington-Kirkpatrick spin glass model
• The infinite-range quantum random Heisenberg magnet
• Collective excitations and marginal stability of quantum Ising spin glasses
• Planckian Metal at a Doping-Induced Quantum Critical Point
• Quantum and thermal fluctuations in the SU(N) Heisenberg spin-glass model near the quantum critical point
• Existence of replica-symmetry breaking in quantum glasses
• Quantum phase transition at non-zero doping in a random $t$-$J$ model
• A Variational Ansatz for the Ground State of the Quantum Sherrington-Kirkpatrick Model
• Quantum fluctuations in the transverse Ising spin glass model: A field theory of random quantum spin systems
• Spin liquid to spin glass crossover in the random quantum Heisenberg magnet
• Dynamical Mean-Field Theory and Aging Dynamics
• Classical-quantum crossover in the critical behavior of the transverse field S-K spin glass model
• Critical metallic phase in the overdoped random $t$-$J$ model
• Quantum quenches in isolated quantum glasses out of equilibrium
• Possible Ergodic-nonergodic regions in the quantum Sherrington-Kirkpatrick spin glass model and quantum annealing
• The de Almeida-Thouless Line in Hierarchical Quantum Spin Glasses

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