The Chiral Gross-Neveu model on the lattice via a Landau-forbidden phase transition

Abstract

We study the phase diagram of the $(1+1)$-dimensional Gross-Neveu model with both $g_x^2(\bar{\psi }\psi {)}^2$ and $g_y^2(\bar{\psi }i{\gamma }_5\psi {)}^2$ interaction terms on a spatial lattice. The continuous chiral symmetry, which is present in the continuum model when $g_x^2=g_y^2$, has a mixed 't~Hooft anomaly with the charge conservation symmetry, which guarantees the existence of a massless mode. However, the same 't~Hooft anomaly also implies that the continuous chiral symmetry is broken explicitly in our lattice model. Nevertheless, from numerical matrix product state simulations we find that, for certain parameters of the lattice model, the continuous chiral symmetry reemerges in the infrared fixed point theory, even at strong coupling. We argue that, to understand this phenomenon, it is crucial to go beyond mean-field theory (or, equivalently, beyond the leading order term in a $1/N$ expansion). Interestingly, on the lattice, the chiral Gross-Neveu model appears at a Landau-forbidden second order phase transition separating two distinct and unrelated symmetry-breaking orders. We point out the crucial role of two different 't Hooft anomalies or Lieb-Schultz-Mattis obstructions for this Landau-forbidden phase transition to occur.

References in corpus (10)

• The density-matrix renormalization group in the age of matrix product states
• "Deconfined" quantum critical points
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Matrix product states represent ground states faithfully
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Scaling in the Fan of an Unconventional Quantum Critical Point
• From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition
• Fermionic Matrix Product States and One-Dimensional Topological Phases
• Deconfined quantum critical point in one dimension
• Quantum phase transitions beyond Landau-Ginzburg theory in one-dimensional space revisited

Cited by in corpus (2)

• Quantum Simulation of the N flavor Gross-Neveu Model
• Phase diagram of the single-flavor Gross--Neveu--Wilson model from the Grassmann corner transfer matrix renormalization group