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We present an accurate numerical algorithm, called quantum belief propagation (QBP), for simulation of one-dimensional quantum systems at non-zero temperature.
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For small enough β \beta , the operator ∫ d ω exp ( β ω ) − 1 ω A ω , s \int{\rm d}\omega\frac{\exp(\beta\omega)-1}{\omega}A^{\omega,s} is local as may be shown by a power series expansion, but at larger β \beta this fails
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M. B. Hastings, Phys. Rev. Lett. 93
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M. B. Hastings, arXiv:0705.2024
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