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arXiv · 1607.04016

Variational tensor network renormalization in imaginary time: benchmark results in the Hubbard model at finite temperature

Piotr Czarnik·Marek M. Rams·Jacek Dziarmaga
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Abstract

A Gibbs operator $e^{-\beta H}$ for a 2D lattice system with a Hamiltonian $H$ can be represented by a 3D tensor network, the third dimension being the imaginary time (inverse temperature) $\beta$. Coarse-graining the network along $\beta$ results in an accurate 2D projected entangled-pair operator (PEPO) with a finite bond dimension. The coarse-graining is performed by a tree tensor network of isometries that are optimized variationally to maximize the accuracy of the PEPO. The algorithm is applied to the two-dimensional Hubbard model on an infinite square lattice. Benchmark results are obtained that are consistent with the best cluster dynamical mean-field theory and power series expansion in the regime of parameters where they yield mutually consistent results.

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Piotr Czarnik, Marek M. Rams, Jacek Dziarmaga. 2016-07-14. Variational tensor network renormalization in imaginary time: benchmark results in the Hubbard model at finite temperature. https://doi.org/10.1103/physrevb.94.235142

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