Symmetric Mass Generation in a Bilayer Honeycomb Lattice with $\mathrm{SU}(2)\times \mathrm{SU}(2)\times \mathrm{SU}(2)/{\mathbb{Z}}_2$ Symmetry

Abstract

A central question beyond the Landau paradigm is the non-perturbative critical theory of the symmetric mass generation (SMG) transition, where strong interactions gap Dirac fermions in (2+1) dimensions without triggering spontaneous symmetry breaking or topological order. While previous studies have already provided evidence for direct SMG transitions in (2+1) dimensions, the fermion scaling dimension -- the key observable for distinguishing candidate critical theories -- has not been determined in a controlled unbiased way. In this Letter, using large-scale determinant quantum Monte Carlo (DQMC) simulations of a bilayer honeycomb lattice model with $\mathrm{SU}(2)\times \mathrm{SU}(2)\times \mathrm{SU}(2)/{\mathbb{Z}}_2$ symmetry, we establish a direct continuous transition by observing the simultaneous opening of single-particle and bosonic gaps at a critical coupling $J_c\approx 2.6$ with correlation length exponent $\nu =1.14(2)$, while an exhaustive search over all 19 symmetry-inequivalent fermion bilinear order parameters confirms the absence of any symmetry breaking. We further obtain the first controlled unbiased estimate of the fermion anomalous dimension, ${\eta }_{\psi }=0.071(1)$, which deviates significantly from the large-$N$ prediction (${\eta }_{\psi }\approx 0.595$) and variational Monte Carlo estimates (${\eta }_{\psi }\approx 0.62$), thereby placing direct quantitative constraints on SMG criticality. By contrasting with a related $\mathrm{Spin}(5)\times \mathrm{U}(1)/{\mathbb{Z}}_2$ model that develops an intermediate excitonic phase, we show that pure non-Abelian symmetry plays a decisive role in stabilizing the direct SMG transition.

Comments: 6+16 pages, 5+9 figures