Low-temperature excitations within the Bethe approximation

@article{Biazzo2013LowtemperatureEW,
  title={Low-temperature excitations within the Bethe approximation},
  author={Indaco Biazzo and Abolfazl Ramezanpour},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2013},
  volume={2013},
  pages={04011}
}
We propose the variational quantum cavity method to construct a minimal energy subspace of wavevectors that are used to obtain some upper bounds for the energy cost of the low-temperature excitations. Given a trial wavefunction we use the cavity method of statistical physics to estimate the Hamiltonian expectation and to find the optimal variational parameters in the subspace of wavevectors orthogonal to the lower-energy wavefunctions. To this end, we write the overlap between two wavefunctions… 

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References

SHOWING 1-10 OF 41 REFERENCES
Sign problem in the Bethe approximation
We propose a message-passing algorithm to compute the Hamiltonian expectation with respect to an appropriate class of trial wave functions for an interacting system of fermions. To this end, we
Cavity approach to variational quantum mechanics
A local and distributive algorithm is proposed to find an optimal trial wave-function minimizing the Hamiltonian expectation in a quantum system. To this end, the quantum state of the system is
The energy density functional formalism for excited states
It is shown that the density can be used as the basic variable for calculating the properties of excited states. The correspondence is not between an eigenstate and its density, as is the case with
Quantum Monte Carlo simulations of solids
This article describes the variational and fixed-node diffusion quantum Monte Carlo methods and how they may be used to calculate the properties of many-electron systems. These stochastic
On quantum mean-field models and their quantum annealing
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
Cavity method for quantum spin glasses on the Bethe lattice
We propose a generalization of the cavity method to quantum spin glasses on fixed connectivity lattices. Our work is motivated by the recent refinements of the classical technique and its potential
The Bethe lattice spin glass revisited
Abstract:So far the problem of a spin glass on a Bethe lattice has been solved only at the replica symmetric level, which is wrong in the spin glass phase. Because of some technical difficulties,
Path-integral representation for quantum spin models: Application to the quantum cavity method and Monte Carlo simulations
The cavity method is a well established technique for solving classical spin models on sparse random graphs (mean-field models with finite connectivity). Laumann et al. [arXiv:0706.4391] proposed
The cavity method for quantum disordered systems: from transverse random field ferromagnets to directed polymers in random media
After reviewing the basics of the cavity method in classical systems, we show how its quantum version, with some appropriate approximation scheme, can be used to study a system of spins with random
Quantum belief propagation: An algorithm for thermal quantum systems
We present an accurate numerical algorithm, called quantum belief propagation, for simulation of one-dimensional quantum systems at nonzero temperature. The algorithm exploits the fact that quantum
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