Tensor Renormalization Group for fermions

Shinichiro Akiyama; Yannick Meurice; Ryo Sakai

doi:10.48550/arxiv.2401.08542

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Tensor Renormalization Group for fermions

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Tensor Renormalization Group for fermions

Shinichiro Akiyama, Yannick Meurice and Ryo Sakai

ArXiv.org

01/16/2024

DOI: 10.48550/arxiv.2401.08542

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https://doi.org/10.48550/arxiv.2401.08542View

Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

We review the basic ideas of the Tensor Renormalization Group method and show how they can be applied for lattice field theory models involving relativistic fermions and Grassmann variables in arbitrary dimensions. We discuss recent progress for entanglement filtering, loop optimization, bond-weighting techniques and matrix product decompositions for Grassmann tensor networks. The new methods are tested with two-dimensional Wilson--Majorana fermions and multi-flavor Gross--Neveu models. We show that the methods can also be applied to the fermionic Hubbard model in 1+1 and 2+1 dimensions.

Physics - High Energy Physics - Lattice

Physics - Quantum Physics

Physics - Statistical Mechanics

Details

Title: Subtitle: Tensor Renormalization Group for fermions
Creators: Shinichiro Akiyama
Yannick Meurice
Ryo Sakai
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2401.08542
ISSN: 2331-8422
Language: English
Date posted: 01/16/2024
Academic Unit: Physics and Astronomy
Record Identifier: 9984548290002771

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