Origin of fermion masses without spontaneous symmetry breaking

TL;DR

The paper addresses whether massless fermions can acquire mass without spontaneous symmetry breaking in a simple three-dimensional lattice four-fermion model, using large-scale fermion-bag Monte Carlo simulations. The authors analyze correlation ratios and monomer densities to identify a quantum critical point at $U_c$ and demonstrate a direct, second-order transition between massless and massive symmetric phases, with no fermion bilinear condensates. They extract critical exponents $\eta \approx 1.05(5)$ and $\nu \approx 1.30(7)$ and show a collapse onto a universal scaling form $R_a(U,L)=L^{-(1+\eta)} g_a((U-U_c)L^{1/\nu})$, suggesting a universal mechanism for fermion mass generation. The results imply a non-traditional mass origin driven by interactions and entanglement/topology, with potential implications for continuum quantum field theory and beyond.

Abstract

Using a simple three dimensional lattice four-fermion model we argue that massless fermions can become massive due to interactions without the need for any spontaneous symmetry breaking. Using large scale Monte Carlo calculations within our model, we show that this non-traditional mass generation mechanism occurs at a second order quantum critical point that separates phases with the same symmetries. Universality then suggests that the new origin for the fermion mass should be of wide interest.

Figures (15)

• Figure 1: The two possible scenarios for the phase diagram of lattice four-fermion models that show the existence of a symmetric massless fermion phase at weak couplings and a symmetric massive fermion phase without spontaneous symmetry breaking at strong couplings. Previous studies in four space-time dimensions found results consistent with scenario A, where an intermediate spontaneously broken phase was found. Our work in three space-time dimensions is consistent with scenario B with a quantum critical point at $U_c$.
• Figure 2: An example of a monomer configuration $[n]$ showing free fermion bags on a two dimensional lattice. The filled circles represent monomers and the connected regions without monomers form free fermion bags.
• Figure 3: Plots of $\rho_m$ and $\chi_1$ as a function of $U$ for various values of $L$. The susceptibility shows a peak and the average monomer density shows a sharp rise at the phase boundary ($U \sim 1$).
• Figure 4: Plot of $R_1$ as a function of $L$ for various values of $U$ near the critical region. The solid lines are fits to the form $1/L^{1+\eta}$ where $\eta$ values are given in table \ref{['eta_Uc_table']}, except at $U=1.03$ where the solid line has the form $\exp(-0.07 L)$ suggesting the fermions are already massive.
• Figure 5: Plots of $R_1$ as a function of $U$ for various lattice sizes showing peaks. The values of the peaks $R_{1,p}$ and their locations $U_{1,p}$ are also marked. These are determined by approximating the function to be a quadratic near the maximum.