Improved coarse-graining methods on two dimensional tensor networks including fermions

Abstract

We show how to apply renormalization group algorithms incorporating entanglement filtering methods and a loop optimization to a tensor network which includes Grassmann variables which represent fermions in an underlying lattice field theory. As a numerical test a variety of quantities are calculated for two dimensional Wilson--Majorana fermions and for the two flavor Gross--Neveu model. The improved algorithms show much better accuracy for quantities such as the free energy and the determination of Fisher's zeros.

arXiv comment21 pages, 21 figures

References in corpus (29)

• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Tensor renormalization group approach to 2D classical lattice models
• Coarse-graining renormalization by higher-order singular value decomposition
• Tensor Network Renormalization
• Second Renormalization of Tensor-Network States
• Grassmann Tensor Renormalization Group Approach to One-Flavor Lattice Schwinger Model
• Renormalization of tensor networks using graph independent local truncations
• Tensor lattice field theory with applications to the renormalization group and quantum computing
• Massive fermions without fermion bilinear condensates
• Tensor renormalization group study of the non-Abelian Higgs model in two dimensions
• Origin of fermion masses without spontaneous symmetry breaking
• Fermion mass without symmetry breaking
• Tensor network formulation of the massless Schwinger model
• Efficient simulation of Grassmann Tensor Product States
• Fermion masses through four-fermion condensates
• Novel phases in strongly coupled four-fermion theories
• The fine structure of the entanglement entropy in the classical XY model
• Tensor Renormalization Group with Randomized Singular Value Decomposition
• Doubling of Entanglement Spectrum in Tensor Renormalization Group
• Fermion masses without symmetry breaking in two spacetime dimensions
• Computing the renormalization group flow of two-dimensional ${\varphi }^4$ theory with tensor networks
• Resolving the Berezinskii-Kosterlitz-Thouless transition in the 2D XY model with tensor-network based level spectroscopy
• Generating a non-perturbative mass gap using Feynman diagrams in an asymptotically free theory
• Chiral Lattice Fermions From Staggered Fields
• Tensor Renormalization Group Algorithms with a Projective Truncation Method
• Benchmark results in the 2D lattice Thirring model with a chemical potential
• Phases of a strongly coupled four-fermion theory
• Tensor network calculation of the logarithmic correction exponent in the XY model
• Ising model as Wilson-Majorana Fermions

Cited by in corpus (3)

• Matrix product decomposition for two- and three-flavor Wilson fermions: Benchmark results in the lattice Gross-Neveu model at finite density
• Forward-mode automatic differentiation for the tensor renormalization group and its relation to the impurity method
• Phase diagram of the single-flavor Gross--Neveu--Wilson model from the Grassmann corner transfer matrix renormalization group