Bond-weighting method for the Grassmann tensor renormalization group

Abstract

Recently, the tensor network description with bond weights on its edges has been proposed as a novel improvement for the tensor renormalization group algorithm. The bond weight is controlled by a single hyperparameter, whose optimal value is estimated in the original work via the numerical computation of the two-dimensional critical Ising model. We develop this bond-weighted tensor renormalization group algorithm to make it applicable to the fermionic system, benchmarking with the two-dimensional massless Wilson fermion. We show that the accuracy with the fixed bond dimension is improved also in the fermionic system and provide numerical evidence that the optimal choice of the hyperparameter is not affected by whether the system is bosonic or fermionic. In addition, by monitoring the singular value spectrum, we find that the scale-invariant structure of the renormalized Grassmann tensor is successfully kept by the bond-weighting technique.

arXiv comment12 pages, 6 figures

References in corpus (21)

• Tensor renormalization group approach to 2D classical lattice models
• Tensor Network Renormalization
• Theory of finite-entanglement scaling at one-dimensional quantum critical points
• Scaling of entanglement support for Matrix Product States
• Review on novel methods for lattice gauge theories
• Loop optimization for tensor network renormalization
• Grassmann Tensor Renormalization Group Approach to One-Flavor Lattice Schwinger Model
• Algorithms for tensor network renormalization
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Critical behavior of lattice Schwinger model with topological term at $\theta =\pi$ using Grassmann tensor renormalization group
• Anisotropic Tensor Renormalization Group
• Tensor lattice field theory with applications to the renormalization group and quantum computing
• Grassmann tensor renormalization group for one-flavor lattice Gross-Neveu model with finite chemical potential
• Berezinskii-Kosterlitz-Thouless transition in lattice Schwinger model with one flavor of Wilson fermion
• Tensor network formulation for two-dimensional lattice $\mathcal{N}=1$ Wess-Zumino model
• Higher order tensor renormalization group for relativistic fermion systems
• Calculation of fermionic Green functions with Grassmann higher-order tensor renormalization group
• Doubling of Entanglement Spectrum in Tensor Renormalization Group
• Restoration of chiral symmetry in cold and dense Nambu--Jona-Lasinio model with tensor renormalization group
• Phase structure of the CP(1) model in the presence of a topological $\theta$-term
• Tensor renormalization group approach to (1+1)-dimensional Hubbard model

Cited by in corpus (9)

• Tensor renormalization group approach to (1+1)-dimensional SU(2) principal chiral model at finite density
• Multi-impurity method for the bond-weighted tensor renormalization group
• Tensor renormalization group study of (1+1)-dimensional U(1) gauge-Higgs model at $\theta =\pi$ with Lüscher's admissibility condition
• Matrix product decomposition for two- and three-flavor Wilson fermions: Benchmark results in the lattice Gross-Neveu model at finite density
• Grassmann tensor renormalization group approach to $(1+1)$-dimensional two-color lattice QCD at finite density
• Triad representation for the anisotropic tensor renormalization group in four dimensions
• Grassmann tensor renormalization group for the massive Schwinger model with a $\theta$ term using staggered fermions
• Tensor renormalization group study of cold and dense QCD in the strong coupling limit
• Phase diagram of the single-flavor Gross--Neveu--Wilson model from the Grassmann corner transfer matrix renormalization group