Semiclassical time crystal in the chiral Gross-Neveu model

TL;DR

This paper demonstrates that the chiral Gross-Neveu model exhibits a semiclassical time crystal phase, where the ground state features a periodic mean field in time at finite fermion current density, breaking temporal translational symmetry.

Contribution

It introduces a novel temporal chiral spiral in the chiral Gross-Neveu model, extending the concept of spatial time crystals to a new quantum field theory context.

Findings

Ground state shows a periodic mean field in time at finite fermion current density.

The model provides an example of a semiclassical time crystal in a quantum field theory.

Temporal symmetry breaking occurs while axial charge remains conserved.

Abstract

In the limit of a large number of flavors, the ground state of the chiral Gross-Neveu model at finite fermion density exhibits a spatially periodic mean field in the form of the chiral spiral, thereby breaking translational invariance. Here we show that the ground state of the same model at finite fermion current density gives rise to a mean field which is periodic in time, a temporal chiral spiral. Since the current density is the same as axial charge density in two dimensions and axial charge is conserved, this may serve as an example of a time crystal. More specifically, as mean field theory is invoked in the large N limit, we are dealing with a semiclassical time crystal.