Finite-time scaling beyond the Kibble-Zurek prerequisite in Dirac systems

TL;DR

This paper extends the finite-time scaling and Kibble-Zurek mechanism to two-dimensional Dirac systems with gapless initial states, revealing new criteria for their applicability in fermionic quantum critical dynamics.

Contribution

It generalizes the Kibble-Zurek theory to include systems with gapless Dirac fermions, relaxing the requirement for a gapped initial state and incorporating composite fluctuations.

Findings

Finite-time scaling applies to gapless initial states in Dirac systems.

A new criterion for the validity of Kibble-Zurek in gapless systems is proposed.

The work broadens understanding of nonequilibrium critical dynamics in fermionic systems.

Abstract

The conventional Kibble-Zurek mechanism and the finite-time scaling provide universal descriptions of the driven critical dynamics from gapped initial states based on the adiabatic-impulse scenario. Here we investigate the driven critical dynamics in two-dimensional Dirac systems, which harbor semimetal and Mott insulator phases separated by the quantum critical point triggered by the interplay between fluctuations of gapless Dirac fermions and order parameter bosons. We find that despite the existence of the gapless initial phase, the driven dynamics can still be captured by the finite-time scaling form. This leads us to propose a criterion for the validity of Kibble-Zurek mechanism with a gapless initial state. Accordingly, our results generalize the Kibble-Zurek theory to incorporate composite fluctuations and relax its requirement for a gapped initial state to systems accommodating gapless Dirac fermionic excitations. Our work not only brings fundamental perspective into the nonequilibrium critical dynamics, but also provides an approach to fathom quantum critical properties in fermionic systems.