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

机译：虚构时间中的变化张量网络重新归一化：基准在有限温度下产生于Hubbard模型

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A Gibbs operator e~(-βH) for a two-dimensional (2D) lattice system with a Hamiltonian H can be represented by a 3D tensor network, with the third dimension being the imaginary time (inverse temperature) β. Coarse graining the network along β results in a 2D projected entangled-pair operator (PEPO) with a finite bond dimension. The coarse graining is performed by a tree tensor network of isometries. They are optimized variationally to maximize the accuracy of the PEPO as a representation of the 2D thermal state e~(-βH). The algorithm is applied to the two-dimensional Hubbard model on an infinite square lattice. Benchmark results at finite temperature 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.

机译：具有哈密顿量H的二维（2D）晶格系统的Gibbs算子e〜（-βH）可以由3D张量网络表示，其中第三维是虚拟时间（逆温度）β。沿β粗化网络会导致二维投影的纠缠对算子（PEPO）具有有限的键维。粗粒化是通过等轴测树的张量网络进行的。对它们进行了可变优化，以最大程度地提高PEPO的精度，以表示2D热态e〜（-βH）。该算法应用于无限方格上的二维Hubbard模型。获得了在有限温度下的基准结果，这些结果与最佳簇动态平均场理论和参数范围内的幂级数展开相一致，从而得出相互一致的结果。

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《Physical review》 |2016年第23期|235142.1-235142.12|共12页
作者
Piotr Czarnik; Marek M. Rams; Jacek Dziarmaga;
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Instytut Fizyki Uniwersytetu Jagiellonskiego, ulica Lojasiewicza 11, PL-30-348 Krakow, Poland;

Instytut Fizyki Uniwersytetu Jagiellonskiego, ulica Lojasiewicza 11, PL-30-348 Krakow, Poland;

Instytut Fizyki Uniwersytetu Jagiellonskiego, ulica Lojasiewicza 11, PL-30-348 Krakow, Poland;

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1. Variational tensor network renormalization in imaginary time: Benchmark results in the Hubbard model at finite temperature [J] . Czarnik Piotr, Rams Marek M., Dziarmaga Jacek Physical review, B . 2016,第23期

机译：虚构时间内的变张量网络重新归一化：基准在有限温度下产生于Hubbard模型
2. Variational tensor network renormalization in imaginary time: Two-dimensional quantum compass model at finite temperature [J] . Piotr Czarnik, Jacek Dziarmaga, Andrzej M. Oles Physical Review. B, Condensed Matter . 2016,第18期

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3. Variational tensor network renormalization in imaginary time: Two-dimensional quantum compass model at finite temperature [J] . Czarnik Piotr, Dziarmaga Jacek, Oles Andrzej M. Physical review, B . 2016,第18期

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7. Variational tensor network renormalization in imaginary time : benchmark results in the Hubbard model at finite temperature [O] . Czarnik, Piotr, Rams, Marek M., Dziarmaga, Jacek 2016

机译：虚构时间中的变张量网络重新归一化：有限温度下的Hubbard模型的基准结果

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

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