Lattice regularisation and entanglement structure of the Gross-Neveu model

Abstract

We construct a Hamiltonian lattice regularisation of the $N$-flavour Gross-Neveu model that manifestly respects the full $\mathsf{O}(2N)$ symmetry, preventing the appearance of any unwanted marginal perturbations to the quantum field theory. In the context of this lattice model, the dynamical mass generation is intimately related to the Coleman-Mermin-Wagner and Lieb-Schultz-Mattis theorem. In particular, the model can be interpreted as lying at the first order phase transition line between a trivial and symmetry-protected topological (SPT) phase, which explains the degeneracy of the elementary kink excitations. We show that our Hamiltonian model can be solved analytically in the large $N$ limit, producing the correct expression for the mass gap. Furthermore, we perform extensive numerical matrix product state simulations for $N=2$, thereby recovering the emergent Lorentz symmetry and the proper non-perturbative mass gap scaling in the continuum limit. Finally, our simulations also reveal how the continuum limit manifests itself in the entanglement spectrum. As expected from conformal field theory we find two conformal towers, one tower spanned by the linear representations of $\mathsf{O}(4)$, corresponding to the trivial phase, and the other by the projective (i.e. spinor) representations, corresponding to the SPT phase.

References in corpus (60)

• Classification of topological insulators and superconductors in three spatial dimensions
• Area laws for the entanglement entropy - a review
• Periodic table for topological insulators and superconductors
• Simulating Lattice Gauge Theories within Quantum Technologies
• A new method to study lattice QCD at finite temperature and chemical potential
• Light pseudoscalar decay constants, quark masses, and low energy constants from three-flavor lattice QCD
• Variational optimization algorithms for uniform matrix product states
• Non-abelian symmetries in tensor networks: a quantum symmetry space approach
• The Non-Abelian Density Matrix Renormalization Group Algorithm
• Solving Gapped Hamiltonians Locally
• Is Entanglement Monogamous?
• The mass spectrum of the Schwinger model with Matrix Product States
• On the Importance of NNLO QCD and Isospin-breaking Corrections in ${\epsilon }^{\prime }/\epsilon$
• Tangent-space methods for uniform matrix product states
• Density Matrix Renormalisation Group Approach to the Massive Schwinger Model
• Matrix product states for gauge field theories
• Variational matrix product ansatz for dispersion relations
• Grassmann Tensor Renormalization Group Approach to One-Flavor Lattice Schwinger Model
• Non-Abelian string breaking phenomena with Matrix Product States
• Exact blocking formulas for spin and gauge models
• Lattice Gauge Tensor Networks
• Matrix Product States: Symmetries and Two-Body Hamiltonians
• Thermal evolution of the Schwinger model with Matrix Product Operators
• Topological vacuum structure of the Schwinger model with matrix product states
• Real-time simulation of the Schwinger effect with Matrix Product States
• Twenty-first Century Lattice Gauge Theory: Results from the QCD Lagrangian
• Matrix product states and variational methods applied to critical quantum field theory
• Chiral condensate in the Schwinger model with Matrix Product Operators
• Critical behavior of lattice Schwinger model with topological term at $\theta =\pi$ using Grassmann tensor renormalization group
• Hamiltonian simulation of the Schwinger model at finite temperature
• Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks
• Transfer Matrices and Excitations with Matrix Product States
• Finite-density phase diagram of a (1+1)-d non-abelian lattice gauge theory with tensor networks
• Grassmann tensor renormalization group for one-flavor lattice Gross-Neveu model with finite chemical potential
• Inhomogeneous phases in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• Berezinskii-Kosterlitz-Thouless transition in lattice Schwinger model with one flavor of Wilson fermion
• A scaling hypothesis for matrix product states
• Building Projected Entangled Pair States with a Local Gauge Symmetry
• Tensor network formulation of the massless Schwinger model
• Universal Entanglement Spectra of Gapped One-dimensional Field Theories
• Gross-Neveu-Wilson model and correlated symmetry-protected topological phases
• O(3) nonlinear sigma model in 1+1 dimensions with matrix product states
• Topological nature of spinons and holons: Elementary excitations from matrix product states with conserved symmetries
• Density matrix renormalization group in a two-dimensional $\lambda {\varphi }^4$ Hamiltonian lattice model
• Tensor Network Simulation of compact one-dimensional lattice Quantum Chromodynamics at finite density
• On Kinks and Bound States in the Gross-Neveu Model
• Phase structure of the interacting Su-Schrieffer-Heeger model and the relationship with the Gross-Neveu model on lattice
• Matrix product representation of gauge invariant states in a Z_2 lattice gauge theory
• Renormalization Group Improved Optimized Perturbation Theory: Revisiting the Mass Gap of the O(2N) Gross-Neveu Model
• Computing the renormalization group flow of two-dimensional ${\varphi }^4$ theory with tensor networks
• Perfect Lattice Actions for the Gross-Neveu Model at large N
• Spinon confinement and deconfinement in spin-1 chains
• BPS kinks in the Gross-Neveu model
• Matrix product states and the nonabelian rotor model
• (Borel) convergence of the variationally improved mass expansion and the O(N) Gross-Neveu model mass gap
• Gauss Law, Minimal Coupling and Fermionic PEPS for Lattice Gauge Theories
• Phase structure of the 1+1 dimensional massive Thirring model from matrix product states
• Tensor renormalization group in bosonic field theory
• Studying a relativistic field theory at finite chemical potential with the density matrix renormalization group
• Dynamical mass generation by source inversion: Calculating the mass gap of the Gross-Neveu model

Cited by in corpus (3)

• Quantum Simulation of the N flavor Gross-Neveu Model
• Large-$N$ Chern insulators: lattice field theory and quantum simulation approaches to correlation effects in the quantum anomalous Hall effect
• Detecting inhomogeneous chiral condensation from the bosonic two-point function in the $(1+1)$-dimensional Gross-Neveu model in the mean-field approximation