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

TL;DR

This study uses large-scale quantum Monte Carlo simulations to investigate a continuous symmetric mass generation transition in a bilayer honeycomb lattice with complex symmetry, providing precise critical exponents and fermion anomalous dimensions.

Contribution

It offers the first controlled unbiased estimate of the fermion anomalous dimension at the SMG transition, challenging previous large-N and variational Monte Carlo predictions.

Findings

Identified a direct continuous SMG transition at J_c ≈ 2.6.

Measured correlation length exponent ν = 1.14(2).

Estimated fermion anomalous dimension η_ψ = 0.071(1).

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.