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).

7 pages, 9 figures

References in corpus (3)

• The performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs
• 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

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• Equilibrium dynamics of infinite-range quantum spin glasses in a field
• Exact Solution for the Transverse Field Sherrington-Kirkpatrick Spin Glass Model with Continuous-Time Quantum Monte Carlo Method
• From quantum-enhanced to quantum-inspired Monte Carlo
• Zero-temperature Monte Carlo simulations of two-dimensional quantum spin glasses guided by neural network states
• Spin-glass quantum phase transition in amorphous arrays of Rydberg atoms
• Chaos controlled and disorder driven phase transitions induced by breaking permutation symmetry
• Trajectory phase transitions in non-interacting systems: all-to-all dynamics and the random energy model
• 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