Low-temperature excitations within the Bethe approximation

Abstract

We propose the variational quantum cavity method to construct a minimal energy subspace of wave vectors that are used to obtain some upper bounds for the energy cost of the low-temperature excitations. Given a trial wave function we use the cavity method of statistical physics to estimate the Hamiltonian expectation and to find the optimal variational parameters in the subspace of wave vectors orthogonal to the lower-energy wave functions. To this end, we write the overlap between two wave functions within the Bethe approximation which allows us to replace the global orthogonality constraint with some local constraints on the variational parameters. The method is applied to the transverse Ising model and different levels of approximations are compared with the exact numerical solutions for small systems.

14 pages, 4 figures

References in corpus (7)

• Gibbs States and the Set of Solutions of Random Constraint Satisfaction Problems
• Quantum Graphical Models and Belief Propagation
• Quantum Belief Propagation
• On the path integral representation for quantum spin models and its application to the quantum cavity method and to Monte Carlo simulations
• Cavity method for quantum spin glasses on the Bethe lattice
• On quantum mean-field models and their quantum annealing
• Sign problem in the Bethe approximation

Cited by in corpus (5)

• The Quantum Cluster Variational Method and the Phase Diagram of the quantum ferromagnetic $J_1$-$J_2$ model
• Quantum Cluster Variational Method and Message Passing Algorithms Revisited
• Bethe free-energy approximations for disordered quantum systems
• Characterizing the parent Hamiltonian for a complete set of orthogonal wave functions: An inverse quantum problem
• Multilayer wave functions: A recursive coupling of local excitations