Novel phases in strongly coupled four-fermion theories

TL;DR

This work analyzes a 4D lattice theory of four massless reduced staggered fermions with an SU(4)-invariant four-fermion interaction. Using auxiliary-field methods and RHMC simulations, it demonstrates the absence of bilinear condensates for all couplings and identifies a strong-coupling phase with a four-fermion condensate and a mass gap that preserves SU(4) symmetry. A narrow region exhibits long-range correlations without symmetry breaking, challenging the conventional view of an intermediate broken phase and opening the possibility of new continuum limits in strongly interacting fermion systems. Finite-volume data and a one-loop Coleman--Weinberg potential support the lack of spontaneous symmetry breaking, though larger-volume studies are needed to confirm the phase structure and critical properties.

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.

Figures (14)

• Figure 1: $\left\langle \frac{1}{4}\sigma_{\pm}^2 \right\rangle -\frac{3}{2}$ vs. $G$ for $L=4$, 6 and 8 with vanishing external sources ($m=0$ in Eq. \ref{['eq:sources']}).
• Figure 2: Site bilinear vs. $G$ for $L = 8$ and 12 with zero external sources.
• Figure 3: $\ln{\chi_{\text{conn}}}$ vs. $G$ for $L=4$, 6, 8 and 12 with zero external sources.
• Figure 4: $\ln{\chi_{\text{conn}}}$ vs. $\ln{L}$ at $G=1.05$ for zero external sources. A least-squares fit to the power law $\chi_{\text{conn}} \propto L^{\gamma}$ yields $\gamma = 3.8(1)$.
• Figure 5: $2\ln{\lambda_{\text{min}}}$ vs. $G$ for $L = 8$ and 12 with zero external sources.