Phase diagram of the single-flavor Gross--Neveu--Wilson model from the Grassmann corner transfer matrix renormalization group

Abstract

We investigate the phase structure of the single-flavor Gross--Neveu model with Wilson fermions using the Grassmann corner transfer matrix renormalization group (CTMRG). The path integral is formulated as a two-dimensional Grassmann tensor network and approximately contracted by the Grassmann CTMRG algorithm. We investigate the phase diagram by varying the fermion mass and the four-fermion coupling, using the pseudoscalar condensate as an order parameter for the ${\mathbb{Z}}_2$ parity symmetry breaking phase. The universality classes of the phase boundaries are identified through the central charge $c$ obtained via scaling analysis of the entanglement entropy. Furthermore, we extract the quantity related to the entanglement spectrum from the converged CTMRG environments, allowing us to distinguish the topological insulator phase and the trivial phase. The resulting phase structure suggests that the Aoki phase is separated from the other phases by critical lines characterized by $c=1/2$, while the critical lines with $c=1$ separate the topological insulating and trivial phases. Our numerical results also indicate that the Aoki phase does not persist in the strong-coupling regime for the single-flavor theory.

26 pages, 20 figures

References in corpus (26)

• Classification of topological insulators and superconductors in three spatial dimensions
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Tensor renormalization group approach to 2D classical lattice models
• Scaling of entanglement support for Matrix Product States
• Grassmann Tensor Renormalization Group Approach to One-Flavor Lattice Schwinger Model
• Simulation of fermionic lattice models in two dimensions with Projected Entangled-Pair States: Next-nearest neighbor Hamiltonians
• 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
• Grassmann tensor renormalization group for one-flavor lattice Gross-Neveu model with finite chemical potential
• Higher order tensor renormalization group for relativistic fermion systems
• Aoki Phases in the Lattice Gross-Neveu Model with Flavored Mass terms
• Restoration of chiral symmetry in cold and dense Nambu--Jona-Lasinio model with tensor renormalization group
• Magnetization of the spin-1/2 Heisenberg antiferromagnet on the triangular lattice
• Grassmann higher-order tensor renormalization group approach for two-dimensional strong-coupling QCD
• Tensor renormalization group approach to (1+1)-dimensional Hubbard model
• Bond-weighting method for the Grassmann tensor renormalization group
• Quantum Simulation of the N flavor Gross-Neveu Model
• Critical behavior of the two-dimensional icosahedron model
• Variational corner transfer matrix renormalization group method for classical statistical models
• GrassmannTN: a Python package for Grassmann tensor network computations
• Improved coarse-graining methods on two dimensional tensor networks including fermions
• Matrix product decomposition for two- and three-flavor Wilson fermions: Benchmark results in the lattice Gross-Neveu model at finite density
• Corner transfer matrix renormalization group analysis of the two-dimensional dodecahedron model
• Phase structure of (3+1)-dimensional dense two-color QCD at $T=0$ in the strong coupling limit with the tensor renormalization group
• Grassmann tensor renormalization group approach to $(1+1)$-dimensional two-color lattice QCD at finite density
• The Chiral Gross-Neveu model on the lattice via a Landau-forbidden phase transition