Quantum fluctuations in the transverse Ising spin glass model: A field theory of random quantum spin systems

Abstract

We develop a mean-field theory for random quantum spin systems using the spin coherent state path integral representation. After the model is reduced to the mean field one-body Hamiltonian, the integral is analyzed with the aid of several methods such as the semiclassical method and the gauge transformation. As an application we consider the Sherrington-Kirkpatrick model in a transverse field. Using the Landau expansion and its improved versions, we give a detailed analysis of the imaginary-time dependence of the order parameters. Integrating out the quantum part of the order parameters, we obtain the effective renormalized free energy written in terms of the classically defined order parameters. Our method allows us to obtain the spin glass-paramagnetic phase transition point $\Gamma /J\sim 1.62$ at T=0.

arXiv comment12 pages, 3 figures; minor changes, proofread for publication

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Cited by in corpus (14)

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• Many body localization-delocalization transition in quantum Sherrington-Kirkpatrick model
• Classical-quantum crossover in the critical behavior of the transverse field S-K spin glass model
• Quantum quenches in isolated quantum glasses out of equilibrium
• Replica symmetry breaking, complexity and spin representation in the generalized random energy model
• Equilibrium dynamics of infinite-range quantum spin glasses in a field
• Dynamical correlations in the Sherrington-Kirkpatrick model in a transverse field
• Effect of random fluctuations on quantum spin-glass transitions at zero temperature
• Effects of low-lying excitations on ground-state energy and energy gap of Sherrington-Kirkpatrick model in transverse field
• The free energy of a quantum Sherrington-Kirkpatrick spin-glass model for weak disorder
• Feynman path integrals for discrete-variable systems: Walks on Hamiltonian graphs
• Replica analysis of partition-function zeros in spin-glass models
• Exact Replica Symmetric solution for transverse field Hopfield model under finite Trotter size