Massive fermions without fermion bilinear condensates

TL;DR

This paper investigates a lattice model with massless fermions and four-fermion interactions, revealing a novel phase where fermions acquire mass without forming bilinear condensates, and identifies a potential second order phase transition.

Contribution

It demonstrates the existence of a strongly coupled massive fermion phase without bilinear condensates and suggests a second order transition, indicating a possible continuum limit in three dimensions.

Findings

Evidence for a second order transition between massless and massive phases.

Fermions become massive without forming bilinear condensates.

Potential continuum limit of the exotic phase in three dimensions.

Abstract

We study a lattice field theory model containing two flavors of massless staggered fermions with an onsite four-fermion interaction. The model contains a $SU(4)$ symmetry which forbids non-zero fermion bilinear mass terms, due to which there is a massless fermion phase at weak couplings. However, even at strong couplings fermion bilinear condensates do not appear in our model, although fermions do become massive. While the existence of this exotic strongly coupled massive fermion phase was established long ago, the nature of the transition between the massless and the massive phase has remained unclear. Using Monte Carlo calculations in three space-time dimensions, we find evidence for a direct second order transition between the two phases suggesting that the exotic lattice phase may have a continuum limit at least in three dimensions. A similar exotic second order critical point was found recently in a bilayer system on a honeycomb lattice.