Novel phases in strongly coupled four-fermion theories

TL;DR

This study investigates a four-fermion lattice model in four dimensions, revealing a novel phase with a four-fermion condensate and mass gap without bilinear condensates, challenging previous models and suggesting new continuum limits.

Contribution

It provides the first evidence of a phase with four-fermion condensates but no bilinear condensates in a four-dimensional lattice model, differing from earlier Higgs--Yukawa studies.

Findings

No bilinear fermion condensates for any coupling value.

Presence of a four-fermion condensate and mass gap at strong coupling.

Absence of a ferromagnetic phase separating phases.

Abstract

We study a lattice model comprising four massless reduced staggered fermions in four dimensions coupled through an $SU(4)$-invariant four-fermion interaction. We present both theoretical arguments and numerical evidence that no bilinear fermion condensates are present for any value of the four-fermi coupling, in contrast to earlier studies of Higgs--Yukawa models with different exact lattice symmetries. At strong coupling we observe the formation of a four-fermion condensate and a mass gap in spite of the absence of bilinear condensates. Unlike those previously studied systems we do not find a ferromagnetic phase separating this strong-coupling phase from the massless weak-coupling phase. Instead we observe long-range correlations in a narrow region of the coupling, still with vanishing bilinear condensates. While our numerical results come from relatively small lattice volumes that call for caution in drawing conclusions, if this novel phase structure is verified by future investigations employing larger volumes it may offer the possibility for new continuum limits for strongly interacting fermions in four dimensions.