Symmetric Mass Generation Transition and its Nonequilibrium Critical Dynamics in a Bilayer Honeycomb Lattice Model

Abstract

Symmetric mass generation (SMG) transitions defy the conventional Landau-Ginzburg-Wilson paradigm by opening a many-body gap without spontaneous symmetry breaking or topological order, attracting intense interest across particle physics and condensed matter physics. Here, we utilize unbiased quantum Monte Carlo simulations to investigate the equilibrium and nonequilibrium critical dynamics of the SMG transition in a bilayer honeycomb lattice model. We unambiguously confirm the existence of an SMG transition at $J_{\text{c}}=2.584(8)$ that separates the Dirac semimetal phase from a symmetry-preserving SMG phase. High-precision extraction of the critical exponents reveals a novel universality class that profoundly departs from mean-field theory. We then extend our study to the nonequilibrium regime, exploring the driven dynamics of the SMG transition. Notably, despite the breakdown of the prerequisites for the celebrated Kibble-Zurek mechanism, the nonequilibrium SMG transition still follows the generalized finite-time scaling. By bridging equilibrium criticality and nonequilibrium dynamics, our work uncovers the universal critical properties of SMG transitions, providing a solid theoretical basis for future experimental studies of SMG physics.

Figures (7)

• Figure 1: Sketch of the phase diagram. The system undergoes a phase transition from DSM to SMG insulator phase at $J_{\text{c}}=2.584(8)$. In the weak-interaction regime ($J < J_{\text{c}}$), the system is in the DSM phase and hosts gapless Dirac fermions. In the strong-interaction regime ($J > J_{\text{c}}$), the fermions acquire an energy gap, driving the system into the SMG phase. The interlayer spin interaction causes interlayer spin singlets (orange ellipse), without breaking the symmetry of the system.
• Figure 2: Determination of critical point and critical properties.(a) The crossing point of $L^{z}\Delta_{\text{sp}}$ as a function of $J$ for various $L$ determines the critical point $J_{\text{c}}=2.584(8)$. (b) The correlation-length exponent $\nu$ is estimated to be $\nu = 0.945(5)$ from the scaling collapse of the rescaled curves of $L^{z}\Delta_{\text{sp}}$ versus $(J-J_{\text{c}})L^{1/\nu}$. (c) The fermion correlation function $G_{\text{AB}}$ at $J_{\text{c}}=2.584(8)$ is shown as a function of system size $L$ on a log-log scale. Power-fitting gives the anomalous dimension $\eta$ as $\eta=0.11(2)$.
• Figure 3: Exclusion of the exciton order.(a) The correlation-length ratio for the exciton order $R_{\text{EC}}$ as a function of $J$ is shown for different system sizes. The lack of crossings in these curves suggests that no phase transition to long-range EC order occurs. (b) The extrapolated results of the exciton structure factor $S_{\text{EC}}$ show that the structure factor tends to zero for $J>J_{\text{c}}$.
• Figure 4: Nonequilibrium dynamic scaling of the SMG transition.(a) Log-log plots of $G_{\text{AB}}$ versus the driving rate $R$ for different $L$ at $J_{\text{c}}=2.584(8)$. The inset in (a) shows $G_{\text{AB}}\propto L^{-2}$ at $R=0.4$, as indicated by the dash-dotted line. For $L=20$, the power-law fit (black solid line) gives $G_{\text{AB}}\propto R^{0.048(6)}$, with an exponent close to $\eta/r=0.053$. (b) In log-log coordinates, the rescaled curves of $G_{\text{AB}}L^{2+\eta}$ versus $RL^r$ collapse onto a single curve, which has a slope close to $\eta/r$ (dashed line). (c) Rescaled curves of $G_{\text{AB}}L^{2+\eta}$ versus $(J-J_{\text{c}})L^{1/\nu}$ for a fixed $RL^{r}=463.92$ and different $L$ collapse onto a single curve.
• Figure S1: Exclusion of CDW, SDW, and SC orders. The results of the structure factors (a)-(c) and correlation-length ratios (d)-(f) for CDW, SDW and SC as a function of $J$ is shown for different system sizes. The lack of crossings in the curves of the correlation-length ratio suggests that no phase transition to long-range CDW, SDW, and SC order occurs.