Dynamical scaling behavior in non-equilibrium quantum phase transitions

We investigate the emergence of universal dynamical scaling in quantum critical spin systems adiabatically driven out of equilibrium, with emphasis on quench dynamics which involves non-isolated critical points ( i.e. , critical regions) and cannot be a priori described through standard scaling arguments nor time-dependent perturbative approaches. Comparing to the case of an isolated quantum critical point, we find that non-equilibrium scaling behavior of a large class of physical observables may still be explained in terms of equilibrium critical exponents. However, the latter are in general non-trivially path-dependent, and detailed knowledge about the time-dependent excitation process becomes essential. In particular, we show how multiple level crossings within a gapless phase may completely suppress excitation depending on the control path. Our results typify non-ergodic scaling in continuous finite-order quantum phase transitions.We investigate the emergence of universal dynamical scaling in quantum critical spin systems adiabatically driven out of equilibrium, with emphasis on quench dynamics which involves non-isolated critical points ( i.e. , critical regions) and cannot be a priori described through standard scaling arguments nor time-dependent perturbative approaches. Comparing to the case of an isolated quantum critical point, we find that non-equilibrium scaling behavior of a large class of physical observables may still be explained in terms of equilibrium critical exponents. However, the latter are in general non-trivially path-dependent, and detailed knowledge about the time-dependent excitation process becomes essential. In particular, we show how multiple level crossings within a gapless phase may completely suppress excitation depending on the control path. Our results typify non-ergodic scaling in continuous finite-order quantum phase transitions.

arXiv:0809.2831Europhysics Letters (EPL)Dec 1, 2008119 citations

Theory of finite-size scaling in dynamical quantum phase transitions

Gui-Zhong Yao, Liang-You Peng, Qihuang Gong

Physical Review ASep 2, 20252 citations

Unique and Universal scaling in dynamical quantum phase transitions

Zhang, Xiang, Liangdong Hu, Fuxiang Li

Universality and scaling are fundamental concepts in equilibrium continuous phase transitions. Here, we unveil a unique and universal scaling behavior of the critical time in slowly driven dynamical quantum phase transition. Going beyond the analogy with equilibrium phase transition, we find that the critical time exhibits a power-law scaling with quenching rate and the scaling exponent is fully determined by underlining universality class. We explain this unique scaling behavior based on the adiabatic-impulse scenario in the Kibble-Zurek mechanism. This universal scaling behavior is verified to be valid not only in noninteracting single-particle system, but also in many-body interacting system, and not only in Hermitian system, but also in non-Hermitian system. Our study unravels a deep and fundamental relationship between dynamical phase transition and equilibrium phase tranition.Universality and scaling are fundamental concepts in equilibrium continuous phase transitions. Here, we unveil a unique and universal scaling behavior of the critical time in slowly driven dynamical quantum phase transition. Going beyond the analogy with equilibrium phase transition, we find that the critical time exhibits a power-law scaling with quenching rate and the scaling exponent is fully determined by underlining universality class. We explain this unique scaling behavior based on the adiabatic-impulse scenario in the Kibble-Zurek mechanism. This universal scaling behavior is verified to be valid not only in noninteracting single-particle system, but also in many-body interacting system, and not only in Hermitian system, but also in non-Hermitian system. Our study unravels a deep and fundamental relationship between dynamical phase transition and equilibrium phase tranition.

arXiv:2409.13293Sep 20, 20240 citations

Scaling Theory of First-Order Quantum Phase Transitions

M. A. Contínentino

Cambridge University Press eBooksJan 1, 20171 citation

Non-equilibrium scaling across first-order transitions with relativistic scalar fields

Leon J. Sieke, Jessica Fuchs, Lorenz von Smekal

We investigate the out-of-equilibrium dynamics of a relativistic $Z_2$ -symmetric scalar field theory with Langevin dynamics in two and three spatial dimensions under linear driving across magnetic first-order phase transitions, close to and far below the critical temperature $T_c$ . Using classical-statistical lattice simulations, we find that if the driving timescale is sufficiently fast, the system exhibits finite-time scaling behavior independent of temperature and dimensionality, identical to that observed in mean-field simulations. In slow quenches near $T_c$ this mean-field behavior crosses over to critical Kibble-Zurek scaling behavior, while for temperatures $T \ll T_c$ nucleation and growth dominate the transition dynamics, resulting in corrections to scaling. Near the transition point where the order parameter changes sign, the crossover between mean-field and critical out-of-equilibrium dynamics is found to be well described by the leading algebraic correction to Kibble-Zurek scaling. We find that universal non-equilibrium scaling behavior can be observed for $T \lesssim T_c$ , provided the driving is fast enough to avoid nucleation but slow enough for correlations to form, and compute the associated universal scaling functions for the order parameter.We investigate the out-of-equilibrium dynamics of a relativistic $Z_2$-symmetric scalar field theory with Langevin dynamics in two and three spatial dimensions under linear driving across magnetic first-order phase transitions, close to and far below the critical temperature $T_c$. Using classical-statistical lattice simulations, we find that if the driving timescale is sufficiently fast, the system exhibits finite-time scaling behavior independent of temperature and dimensionality, identical to that observed in mean-field simulations. In slow quenches near $T_c$ this mean-field behavior crosses over to critical Kibble-Zurek scaling behavior, while for temperatures $T \ll T_c$ nucleation and growth dominate the transition dynamics, resulting in corrections to scaling. Near the transition point where the order parameter changes sign, the crossover between mean-field and critical out-of-equilibrium dynamics is found to be well described by the leading algebraic correction to Kibble-Zurek scaling. We find that universal non-equilibrium scaling behavior can be observed for $T \lesssim T_c$, provided the driving is fast enough to avoid nucleation but slow enough for correlations to form, and compute the associated universal scaling functions for the order parameter.

arXiv:2605.10346May 11, 20260 citations

Dynamical Quantum Phase Transitions

Ralf Schützhold

arXiv:1004.2409Journal of Low Temperature PhysicsOct 29, 200812 citations

We investigate the out-of-equilibrium dynamics of a relativistic

Z_2

-symmetric scalar field theory with Langevin dynamics in two and three spatial dimensions under linear driving across magnetic first-order phase transitions, close to and far below the critical temperature

T_c

. Using classical-statistical lattice simulations, we find that if the driving timescale is sufficiently fast, the system exhibits finite-time scaling behavior independent of temperature and dimensionality, identical to that observed in mean-field simulations. In slow quenches near

T_c

this mean-field behavior crosses over to critical Kibble-Zurek scaling behavior, while for temperatures

T \ll T_c

nucleation and growth dominate the transition dynamics, resulting in corrections to scaling. Near the transition point where the order parameter changes sign, the crossover between mean-field and critical out-of-equilibrium dynamics is found to be well described by the leading algebraic correction to Kibble-Zurek scaling. We find that universal non-equilibrium scaling behavior can be observed for

T \lesssim T_c

, provided the driving is fast enough to avoid nucleation but slow enough for correlations to form, and compute the associated universal scaling functions for the order parameter.