Driven Critical Dynamics in Strongly Interacting Dirac Systems

Abstract: The conventional Kibble-Zurek mechanism (KZM) and finite-time scaling (FTS) provide universal descriptions of the driven critical dynamics from gapped initial states based on the adiabatic-impulse scenario. In this paper, by leveraging the large-scale quantum Monte Carlo simulation, we investigate the driven critical dynamics in two-dimensional Dirac systems, which harbor semimetal and Mott insulator phases separated by the quantum critical point (QCP) triggered by the interplay between fluctuations of gapless Dirac fermions and order parameter bosons. A remarkable discovery is that, despite the existence of the gapless initial phase, the driven dynamics can still be captured by the FTS form. This leads us to propose a generalized criterion for the validity of KZM and FTS with a gapless initial state. Accordingly, our results significantly generalize the KZM theory to incorporate composite fluctuations and relax its requirement for a gapped initial state to systems accommodating gapless Dirac fermionic excitations. Through successfully extending the KZM and FTS theory to the strongly interacting Dirac QCP, our work not only brings new fundamental perspective into the nonequilibrium critical dynamics, but also provides a novel theoretical approach to fathom quantum critical properties in fermionic systems.