Nonequilibrium work on spin glasses in longitudinal and transverse fields

Abstract

We derive a number of exact relations between equilibrium and nonequilibrium quantities for spin glasses in external fields using the Jarzynski equality and gauge symmetry. For randomly-distributed longitudinal fields, a lower bound is established for the work done on the system in nonequilibrium processes, and identities are proven to relate equilibrium and nonequilibrium quantities. In the case of uniform transverse fields, identities are proven between physical quantities and exponentiated work done to the system at different parts of the phase diagram with the context of quantum annealing in mind. Additional relations are given, which relate the exponentiated work in quantum and simulated (classical) annealing. It is also suggested that the Jarzynski equality may serve as a guide to develop a method to perform quantum annealing under non-adiabatic conditions.

17 pages, 5 figures, submitted to JPSJ

References in corpus (8)

• Mathematical Foundation of Quantum Annealing
• Fluctuation Theorem for Arbitrary Open Quantum Systems
• First order phase transition in the Quantum Adiabatic Algorithm
• Escorted Free Energy Simulations: Improving Convergence by Reducing Dissipation
• Simple Glass Models and their Quantum Annealing
• Quantum annealing with Jarzynski equality
• Gauge Theory for Quantum Spin Glasses
• Non-equilibrium Relations for Spin Glasses with Gauge Symmetry

Cited by in corpus (6)

• Benchmark test of Black-box optimization using D-Wave quantum annealer
• Statistical-mechanical analysis of compressed sensing for Hamiltonian estimation of Ising spin glass
• Message-passing algorithm of quantum annealing with nonstoquastic Hamiltonian
• Fluctuation Theorems on Nishimori Line
• Proposal of a Checking Parameter in the Simulated Annealing Method Applied to the Spin Glass Model
• Statistical mechanical models of integer factorization problem