Symmetric Mass Generation via Multicriticality in a 3D Lattice Gross-Neveu Model

Abstract

We investigate a three-dimensional lattice model of two flavors of massless staggered fermions coupled through two independent four-fermion interactions, $U_I$ and $U_B$. Using large-scale fermion-bag Monte Carlo simulations, we map out the phase diagram in the $(U_I, U_B)$ parameter space and identify three distinct phases: a massless fermion phase, a symmetry-broken massive phase, and a symmetric massive phase. When one of the interactions is absent ($U_B=0$), the system undergoes a single continuous transition directly connecting the massless and symmetric massive phases, a feature previously associated with unconventional fermion mass generation. We find that turning on a nonzero $U_B$ separates this direct transition into two successive transitions with an intermediate symmetry-broken phase. The transition from the massless to the broken phase belongs to the Gross-Neveu universality class, while the transition from the broken to the symmetric massive phase falls into the three-dimensional XY universality class. Our results indicate that the special point at vanishing coupling, where the direct transition occurs, plays the role of a multicritical point organizing the surrounding phase structure. These findings provide a unified lattice perspective on conventional and unconventional mechanisms of fermion mass generation within a single model.

Figures (5)

• Figure 1: Example of a $[b,i]$ configuration on a $2^3$ lattice. Red circles show instantons, red links show bonds or dimers, and black circles indicate free sites.
• Figure 2: Thermalization histories of the bond density ($\rho_u$) (left), the instanton density ($\rho_I$) (middle), and the susceptibility ($\chi_{ud}$) (right) as functions of Monte Carlo steps for three different values of the reweighting parameter $\Omega = 1, 10,$ and $20$, on a $44^3$ lattice at $U_B=0.1$ and $U_I=0.6$.
• Figure 3: The phase diagram of our model in the $U_I$ and $U_B$ plane.
• Figure 4: (Top) Heat-map of $\chi_{ud}$ in the $(U_B,U_I)$ plane for lattice sizes $L=12,16,$ and $20$. (Bottom) $\chi_{ud}$ as a function of $U_I$ at fixed $U_B=0.0,\,0.1,$ and $0.2$.
• Figure 5: Finite-size scaling collapse from Eq. \ref{['eq:eq-fss']} at $U_B=0.1$. (Left): Gross–Neveu transition with a fourth-order polynomial fit and freely varying critical exponents. (Right): 3D–XY transition; the solid line (Fit 1) corresponds to the fit with $\nu$ and $\eta$ treated as fit parameters, while the dashed line (Fit 2) shows the collapse obtained by fixing the exponents to their known 3D–XY values PhysRevB.63.214503.