Work

More about the Grassmann tensor renormalization group

Year: 2021

Type: article

Abstract: We derive a general formula of the tensor network representation for d-dimensional lattice fermions with ultra-local interactions, including Wilson fermions, staggered fermions, and domain-wall fermions. The Grassmann tensor is concretely defined with auxiliary Grassmann variables that play a role in bond degrees of freedom. Compared to previous works, our formula does not refer to the details of lattice fermions and is derived by using the singular value decomposition for the given Dirac matrix without any ad-hoc treatment for each fermion. We numerically test our formula for free Wilson and staggered fermions and find that it properly works for them. We also find that Wilson fermions show better performance than staggered fermions in the tensor renormalization group approach, unlike the Monte Carlo method.

Source: Journal of High Energy Physics

DOI: 10.1007/jhep10(2021)188

Authors: Shinichiro Akiyama, Daisuke Kadoh

Institutions: University of Tsukuba, Keio University, National Tsing Hua University, National Center for Theoretical Sciences, Physics Division

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

Funder: Japan Society for the Promotion of Science

Awards: New frontier of numerical supersymmetry led by supersymmetric gradient flows, Tensor renormalization group study of (3+1)-dimensional systems with the sign problem