Quantum Belief Propagation

Details Quantum Belief Propagation Quantum Belief Propagation

2007-06-28

arxiv.org/abs/0706.4094v3

Phys. Rev. B Rapids 76, 201102 (2007)

Physics

Condensed Matter

Strongly Correlated Electrons

4 pages, 1 figure; revised time estimates due to improved implementation. Typographical corrections to Eq. 7 made; thanks to D

Scientific paper

10.1103/PhysRevB.76.201102

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.

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