On quantum mean-field models and their quantum annealing

2012/03/31 by Victor Bapst, Guilhem Semerjian · 2 citations
Computer Science · Physics and Astronomy · #Adiabatic process #Ferromagnetism #Metastability #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum annealing #Quantum dynamics #Quantum many-body systems #Quantum phase transition #Quantum phases #Spinodal #Spins #cond-mat.dis-nn #cond-mat.stat-mech #quant-ph

paper · pdf · doi:10.1088/1742-5468/2012/06/p06007

published as J. Stat. Mech. P06007 (2012) · 44 pages, 23 figures

openalex publication_date 2012/06/19 · arxiv created 2012/07/25 · arxiv updated 2012/07/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

This paper deals with fully-connected mean-field models of quantum spins with p-body ferromagnetic interactions and a transverse field. For p=2 this corresponds to the quantum Curie-Weiss model (a special case of the Lipkin-Meshkov-Glick model) which exhibits a second-order phase transition, while for p>2 the transition is first order. We provide a refined analytical description both of the static and of the dynamic properties of these models. In particular we obtain analytically the exponential rate of decay of the gap at the first-order transition. We also study the slow annealing from the pure transverse field to the pure ferromagnet (and vice versa) and discuss the effect of the first-order transition and of the spinodal limit of metastability on the residual excitation energy, both for finite and exponentially divergent annealing times. In the quantum computation perspective this quantity would assess the efficiency of the quantum adiabatic procedure as an approximation algorithm.

Citations

• Validity of many-body approximation methods for a solvable model
• Entanglement dynamics in the Lipkin-Meshkov-Glick model
• Quantum Annealing in the Transverse Ising Model
• Dynamics of a quantum phase transition and relaxation to a steady state
• Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• Quantum stochastic optimization
• Cavity method for quantum spin glasses on the Bethe lattice
• Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
• Simple Glass Models and Their Quantum Annealing
• Optimization using quantum mechanics: quantum annealing through adiabatic evolution
• Semiclassical analysis of spin systems near critical energies
• Analytical results for state-to-state transition probabilities in the multistate Landau-Zener model by nonstationary perturbation theory
• The Phase Diagram of the Quantum Curie-Weiss Model
• Path-integral representation for quantum spin models: Application to the quantum cavity method and Monte Carlo simulations
• Proof verification and the hardness of approximation problems
• Quantum Search by Local Adiabatic Evolution
• Gibbs states and the set of solutions of random constraint satisfaction problems

Cited by

• Integrable, Mixed, and Chaotic Dynamics in a Single All-to-All Ising Spin Model
• Ensemble Inequivalence in Long-Range Quantum Spin Systems