Stability of the quantum Sherrington-Kirkpatrick spin glass model

Abstract

We study in detail the quantum Sherrington-Kirkpatrick (SK) model, i.e. the infinite-range Ising spin glass in a transverse field, by solving numerically the effective one-dimensional model that the quantum SK model can be mapped to in the thermodynamic limit. We find that the replica symmetric (RS) solution is unstable down to zero temperature, in contrast to some previous claims, and so there is not only a line of transitions in the (longitudinal) field-temperature plane (the de Almeida-Thouless, AT, line) where replica symmetry is broken, but also a quantum de Almeida-Thouless (QuAT) line in the transverse field-longitudinal field plane at $T=0$. If the QuAT line also occurs in models with short-range interactions its presence might affect the performance of quantum annealers when solving spin glass-type problems with a bias (i.e. magnetic field).

arXiv comment7 pages, 9 figures

References in corpus (12)

• Quantum Annealing in the Transverse Ising Model
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Defining and detecting quantum speedup
• Landau theory of quantum spin glasses of rotors and Ising spins
• A Solvable Spin-Glass of Quantum Rotors
• The performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs
• Exponential Complexity of the Quantum Adiabatic Algorithm for certain Satisfiability Problems
• Best-case performance of quantum annealers on native spin-glass benchmarks: How chaos can affect success probabilities
• Classical-quantum crossover in the critical behavior of the transverse field S-K spin glass model
• Possible Ergodic-nonergodic regions in the quantum Sherrington-Kirkpatrick spin glass model and quantum annealing
• Critical and Griffiths-McCoy singularities in quantum Ising spin-glasses on d-dimensional hypercubic lattices: A series expansion study
• Notes on the replica symmetric solution of the classical and quantum SK model, including the matrix of second derivatives and the spin glass susceptibility

Cited by in corpus (20)

• Quantum Annealing: An Overview
• Finding spin-glass ground states using quantum walks
• Entanglement and replica symmetry breaking in a driven-dissipative quantum spin glass
• Existence of replica-symmetry breaking in quantum glasses
• A Variational Ansatz for the Ground State of the Quantum Sherrington-Kirkpatrick Model
• Many-body localization enables iterative quantum optimization
• Many body localization-delocalization transition in quantum Sherrington-Kirkpatrick model
• Possible Ergodic-nonergodic regions in the quantum Sherrington-Kirkpatrick spin glass model and quantum annealing
• Quantum Jamming: Critical Properties of a Quantum Mechanical Perceptron
• 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
• From quantum-enhanced to quantum-inspired Monte Carlo
• Trajectory phase transitions in non-interacting systems: all-to-all dynamics and the random energy model
• Spin-glass quantum phase transition in amorphous arrays of Rydberg atoms
• Zero-temperature Monte Carlo simulations of two-dimensional quantum spin glasses guided by neural network states
• Chaos controlled and disorder driven phase transitions induced by breaking permutation symmetry
• The free energy of a quantum Sherrington-Kirkpatrick spin-glass model for weak disorder
• Exact Replica Symmetric solution for transverse field Hopfield model under finite Trotter size
• Energy gap of quantum spin glasses: a projection quantum Monte Carlo study