Lattice regularisation and entanglement structure of the Gross-Neveu model

TL;DR

This paper develops a lattice Hamiltonian for the Gross-Neveu model that preserves its symmetries, enabling analytical and numerical studies of mass generation, phase structure, and entanglement properties in the continuum limit.

Contribution

It introduces a symmetry-preserving lattice regularisation of the Gross-Neveu model and analyzes its phase transition and entanglement structure using analytical and numerical methods.

Findings

Correct mass gap expression in large N limit

Emergent Lorentz symmetry in N=2 simulations

Identification of conformal towers in entanglement spectrum

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.