Symmetric mass generation as a multicritical point with enhanced symmetry

Abstract

We explore the phase diagram of a lattice fermion model that exhibits three distinct phases: a massless fermion (MF) phase; a massive fermion phase with spontaneous symmetry breaking (SSB) induced by a fermion bilinear condensate; and a massive fermion phase with symmetric mass generation (SMG). Using the fermion-bag Monte Carlo method on large cubical lattices, we find evidence for traditional second-order critical points separating the first two and the latter two phases. Remarkably, these critical points appear to merge at a multicritical point with enhanced symmetry when the symmetry breaking parameter is tuned to zero, giving rise to the recently discovered direct second-order transition between the massless and symmetric massive fermion phases.

Figures (4)

• Figure 1: Phase diagram of the two-flavor massless staggered fermion model in three space-time dimensions with two four-fermion couplings, as defined in \ref{['eq:model-2']}. The generic internal symmetry ${\mathrm{SU}}(2)\times {\mathrm{SU}}(2)\times U_\chi(1)$ is enhanced to ${\mathrm{SU}}(4)$ along the $U_B=0$ axis. The critical point on this axis, which appears as a direct second-order transition between the and phases, is in fact a multicritical point where the Gross--Neveu and 3D XY critical lines merge. In the phase the $U_\chi(1)$ symmetry is broken spontaneously.
• Figure 2: Plots of the critical finite-size scaling function defined in \ref{['eq:crit-scaling']} at the Gross--Neveu transition (left panel) and the 3D-XY transition (right panel) for $U_B = 0.1$. The solid lines represent polynomial fits: a fourth-order polynomial for the Gross--Neveu case and a linear fit for the 3D-XY case. For the Gross--Neveu transition, the critical coupling and critical exponents are treated as fit parameters, whereas for the 3D-XY transition the critical exponents are fixed to their known values. The Monte Carlo data, shown with error bars, were obtained for various lattice sizes $L$ and a range of couplings $U_I$ in the vicinity of the respective critical points.
• Figure 3: Evidence for the phase diagram shown in \ref{['fig:phase-diag']}. Shown are heat maps of the susceptibility $\chi_{ud}$ at three lattice sizes, illustrating the structure of the phase diagram. Enhanced susceptibilities indicative of an phase are visible for $U_B$ values as small as $U_B = 0.01$ at $U_I = 1.0$ (see MaitiPRDcomp).
• Figure 4: Conjectured RG flows in three dimensions for fermionic Gross--Neveu--Yukawa models near the fixed point. Our results indicate four fixed points: the Gaussian fixed point (massless fermions, massive bosons); a Gross--Neveu fixed point (interacting massless fermions and bosons, one relevant direction); an XY fixed point (interacting massless bosons, one relevant direction); and the new fixed point, which has two relevant directions but reduces to one when an additional symmetry is imposed.