Massive fermions without fermion bilinear condensates

TL;DR

This work identifies an exotic mechanism of fermion mass generation in a 3D lattice field theory of two staggered fermion flavors with onsite four-fermion interactions and an $SU(4)$ symmetry that forbids bilinear masses. Using a sign-problem-free fermion bag Monte Carlo approach, the authors demonstrate a direct second-order transition between a massless PMW phase and a massive PMS phase without bilinear condensates, suggesting a possible continuum limit. The study connects to lattice Yukawa models and an analogous transition in bilayer honeycomb systems, highlighting a novel, symmetry-protected route to mass generation driven by dynamics rather than spontaneous symmetry breaking. These results motivate further theoretical work to identify the continuum field theory governing the critical point and to explore extensions to higher dimensions and related lattice systems.

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.

Figures (7)

• Figure 1: The two possible phase diagrams for our model based on previous studies. Our work provides strong evidence in favor of scenario B with a second order transition between the PMW phase and the PMS phase.
• Figure 2: An example of a monomer configuration $[n]$ showing free fermion bags on a two dimensional lattice.
• Figure 3: Plots of equilibration for the three observables $\rho_m$, $\chi_1$ and $\chi_2$, starting from a configuration with zero monomers at $L=20$, $U=0.95$. The insets show the Monte Carlo time history for 900 sweeps using ALG2. The average of the data from the inset is shown as a solid line in the main plots. The open squares are average data from 500 independent runs after a single sweep starting from an equilibrated configuration. The plot demonstrates that instead of running a single computer for many sweeps, one can run many computers for a single sweep and average the data.
• Figure 4: The variation of the monomer density $\rho_m$ (a four-point condensate) as a function of $U$ at $L=8,12$ and $16$. The inset shows the change in $\rho_m$ as a function of $L$ at $U=1.0,1.1$ and $1.2$ where the variation is the maximum. By $L=16$ we find that $\rho_m$ has reached its thermodynamic limit at all values of $U$.
• Figure 5: Plots of the susceptibilities $\chi_1$ (left) and $\chi_2$ (right) as a function of the coupling constant $U$ for lattice sizes ranging from $L=8$ to $L=28$. The inset shows the finite size scalings in the critical region. There is no sign of the $L^3$ divergence expected in the presence of a non-zero fermion bilinear condensate. A roughly linear divergence appears in the critical region consistent with a second order critical scaling.