Scaling corrections in driven critical dynamics: Application to a two-dimensional dimerized quantum Heisenberg model

TL;DR

This paper investigates how scaling corrections influence driven critical dynamics in a 2D quantum Heisenberg model, emphasizing the importance of incorporating finite size and rate effects for accurate nonequilibrium scaling descriptions.

Contribution

It introduces a comprehensive finite-time scaling form that includes corrections from system size and driving rate, validated through numerical simulations.

Findings

Scaling corrections are essential for accurate nonequilibrium descriptions.

Improved scaling relations are derived from full scaling form expansion.

Numerical verification confirms the validity of the proposed scaling forms.

Abstract

Driven critical dynamics in quantum phase transitions holds significant theoretical importance, and also practical applications in fast-developing quantum devices. While scaling corrections have been shown to play important roles in fully characterizing equilibrium quantum criticality, their impact on nonequilibrium critical dynamics has not been extensively explored. In this work, we investigate the driven critical dynamics in a two-dimensional quantum Heisenberg model. We find that in this model the scaling corrections arising from both finite system size and finite driving rate must be incorporated into the finite-time scaling form in order to properly describe the nonequilibrium scaling behaviors. In addition, improved scaling relations are obtained from the expansion of the full scaling form. We numerically verify these scaling forms and improved scaling relations for different starting states using the nonequilibrium quantum Monte Carlo algorithm.