Nonequilibrium Dynamics of Dirac Quantum Criticality in Imaginary Time

Abstract

Quantum criticality within Dirac fermions harbors a plethora of exotic phenomena, attracting sustained attention in the past decades. Here, we explore the imaginary-time relaxation dynamics in a typical Dirac quantum criticality belonging to chiral Heisenberg universality class. Performing large-scale quantum Monte Carlo simulation, we unveil rich nonequilibrium critical phenomena from different initial states. In particular, we identify a non-stationary initial slip evolution characterized by an unconventional negative critical exponent $θ=-0.84(4)$, corroborating the significant impact of fermionic critical fluctuations. Furthermore, we generalize the nonequilibrium scaling theory to incorporate both fermionic and bosonic critical modes, capturing their distinct relaxation behaviors. Armed with the scaling theory, we establish a new framework to investigate fermionic quantum criticality based on short-time dynamics, paving a promising avenue to fathoming quantum criticality in diverse fermionic systems with high efficiency.

Figures (13)

• Figure 1: Sketch of the phase diagram and the quench protocol in imaginary-time with different initial states. The initial states are prepared as (i) the Dirac semimetal (DSM) phase, (ii) the saturated AFM state, and (iii) the random spin (RS) state. All states correspond to the fixed points of the initial states under the renormalization group transformation.
• Figure 2: The results of correlation-length ratio $R$ against interaction $U$ for various sizes during the short-time stage, with a fixed value of $\tau L^{-z}$. (a) Estimation of the critical point via the intersection points of curves for $\tau L^{-z}=0.3$ (Main panel), $0.34$ and $0.5$ (Inset). (b) Estimation of $\nu$ by scaling collapse analysis of correlation-length ratio.
• Figure 3: Relaxation dynamics at QCP with the AFM initial state. (a) Curves of $m^2$ versus $\tau$ for different sizes before (a1) and after (a2) rescaling. The dashed line in (a1) representing $m^2\propto \tau^{-2\beta/\nu z}$ with $\beta/\nu$ estimated from (a2) is plotted for comparison. (b) Curves of $G$ versus $\tau$ before (b1) and after (b2) rescaling. The dashed line in (b1) represents $G\propto \tau^{1-\eta_\psi/z}$ with $\eta_\psi$ estimated from (b2).
• Figure 4: Relaxation dynamics at QCP with the DSM initial state. (a) Curves of $m^2$ versus $\tau$ at the critical point for different sizes before (a1) and after (a2) rescaling. The dashed line representing $m^2\propto \tau^{d/z-2\beta/\nu z}$ is plotted in (a1) for comparison. (b) Curves of $G$ versus $\tau$ before (b1) and after (b2) rescaling. The dashed line in (b1) represents $G\propto \tau^{-\eta_\psi/z}$. The critical exponents used here are estimated from Fig. \ref{['figure3']}.
• Figure 5: Critical initial slip manifested in the evolution of the auto-correlation function $A$ with the RS initial state. Curves of $A$ versus $\tau$ for different sizes at the critical point before (a) and after (b) rescaling.