Quantum Belief Propagation

Abstract

We present an accurate numerical algorithm, called quantum belief propagation (QBP), for simulation of one-dimensional quantum systems at non-zero temperature. The algorithm exploits the fact that quantum effects are short-range in these systems at non-zero temperature, decaying on a length scale inversely proportional to the temperature. We compare to exact results on a spin-1/2 Heisenberg chain. Even a very modest calculation, requiring diagonalizing only 10-by-10 matrices, reproduces the peak susceptibility with a relative error of less than $10^{-5}$, while more elaborate calculations further reduce the error.

4 pages, 1 figure; revised time estimates due to improved implementation. Typographical corrections to Eq. 7 made; thanks to David Poulin for pointing out the mistake

References in corpus (2)

• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Lieb-Robinson Bounds and the Exponential Clustering Theorem

Cited by in corpus (8)

• 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
• Complexity of thermal states in quantum spin chains
• Sequentially generated states for the study of two dimensional systems
• Observations Outside the Light-Cone: Algorithms for Non-Equilibrium and Thermal States
• Belief propagation algorithm for computing correlation functions in finite-temperature quantum many-body systems on loopy graphs
• Griffiths-McCoy singularities, Lee-Yang zeros and the cavity method in a solvable diluted ferromagnet
• Quantum serial turbo-codes