Existence of replica-symmetry breaking in quantum glasses

Abstract

By controlling quantum fluctuations via the Falk-Bruch inequality we give the first rigorous argument for the existence of a spin-glass phase in the quantum Sherrington-Kirkpatrick model with a transverse magnetic field if the temperature and the field are sufficiently low. The argument also applies to the generalization of the model with multi-spin interactions, sometimes dubbed as transverse $p$-spin model.

Argument extended up to the zero-field critical temperature; publication information added

References in corpus (6)

• Many-body mobility edge in a mean-field quantum spin glass
• The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective
• Clustering of non-ergodic eigenstates in quantum spin glasses
• Stability of the quantum Sherrington-Kirkpatrick spin glass model
• Thermodynamics and Universality for Mean Field Quantum Spin Glasses
• Phase diagram of the $p$-spin-interacting spin glass with ferromagnetic bias and a transverse field in the infinite-$p$ limit

Cited by in corpus (15)

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• A Variational Ansatz for the Ground State of the Quantum Sherrington-Kirkpatrick Model
• Eigenstate localization in a many-body quantum system
• Spectral Analysis of the Quantum Random Energy Model
• The de Almeida-Thouless Line in Hierarchical Quantum Spin Glasses
• Exact Solution for the Transverse Field Sherrington-Kirkpatrick Spin Glass Model with Continuous-Time Quantum Monte Carlo Method
• Equilibrium dynamics of infinite-range quantum spin glasses in a field
• Boundedness of Susceptibility in Spin Glass Transition of Transverse Field Mixed $p$-spin Glass Models
• Spin-glass quantum phase transition in amorphous arrays of Rydberg atoms
• Trajectory phase transitions in non-interacting systems: all-to-all dynamics and the random energy model
• Zero-temperature Monte Carlo simulations of two-dimensional quantum spin glasses guided by neural network states
• Development of research network on Quantum Annealing Computation and Information using Google Scholar data
• Gauge theory for quantum XYZ spin glasses
• Extended Series of Correlation Inequalities in Quantum Systems