We investigate the dynamic behavior of finite-size systems close to a first-order transition (FOT). We develop a dynamic finite-size scaling (DFSS) theory for the dynamic behavior in the coexistence region where different phases coexist. This is characterized by an exponentially large time scale related to the tunneling between the two phases. We show that, when considering time scales of the order of the tunneling time, the dynamic behavior can be described by a two-state coarse-grained dynamics. This allows us to obtain exact predictions for the dynamical scaling functions. To test the general DFSS theory at FOTs, we consider the two-dimensional Ising model in the low-temperature phase, where the external magnetic field drives a FOT, and the 20-state Potts model, which undergoes a thermal FOT. Numerical results for a purely relaxational dynamics fully confirm the general theory.We investigate the dynamic behavior of finite-size systems close to a first-order transition (FOT). We develop a dynamic finite-size scaling (DFSS) theory for the dynamic behavior in the coexistence region where different phases coexist. This is characterized by an exponentially large time scale related to the tunneling between the two phases. We show that, when considering time scales of the order of the tunneling time, the dynamic behavior can be described by a two-state coarse-grained dynamics. This allows us to obtain exact predictions for the dynamical scaling functions. To test the general DFSS theory at FOTs, we consider the two-dimensional Ising model in the low-temperature phase, where the external magnetic field drives a FOT, and the 20-state Potts model, which undergoes a thermal FOT. Numerical results for a purely relaxational dynamics fully confirm the general theory.

arXiv:1705.03198Physical review. EJul 12, 201714 citations

The dynamical bulk boundary correspondence and dynamical quantum phase transitions in the Benalcazar–Bernevig–Hughes model

Tomasz Masłowski, Nicholas Sedlmayr

In this article we demonstrate that dynamical quantum phase transitions (DQPTs) occur for an exemplary higher order topological insulator, the Benalcazar-Bernevig-Hughes model, following quenches across a topological phase boundary. A dynamical bulk boundary correspondence is also seen both in the eigenvalues of the Loschmidt overlap matrix and the boundary return rate. The latter is found from a finite size scaling analysis for which the relative simplicity of the model is crucial. Contrary to the usual two dimensional case the DQPTs in this model show up as cusps in the return rate, as for a one dimensional model, rather than as cusps in its derivative as would be typical for a two dimensional model. We explain the origin of this behaviour.In this article we demonstrate that dynamical quantum phase transitions (DQPTs) occur for an exemplary higher order topological insulator, the Benalcazar-Bernevig-Hughes model, following quenches across a topological phase boundary. A dynamical bulk boundary correspondence is also seen both in the eigenvalues of the Loschmidt overlap matrix and the boundary return rate. The latter is found from a finite size scaling analysis for which the relative simplicity of the model is crucial. Contrary to the usual two dimensional case the DQPTs in this model show up as cusps in the return rate, as for a one dimensional model, rather than as cusps in its derivative as would be typical for a two dimensional model. We explain the origin of this behaviour.

Journal of Physics Condensed MatterMay 11, 20243 citations

Nonequilibrium Dynamical Quantum Phase Transitions in the Extended Agassi Model

Ritesh Kumar Palai, Rajiv Kumar, Venktesh Singh +1 more

We investigate dynamical quantum phase transitions (DQPTs) in the extended Agassi model following sudden quenches of same level pairing ( $Σ$ ), monopole-monopole ( $χ$ ) and cross level pairing ( $Λ$ ) strengths. Using exact diagonalization, we characterize the non-equilibrium dynamics through the Loschmidt echo and intensive return-rate function. Quenches across equilibrium phase boundaries produce cusp-like structures in the return rate that shows non-analyticities with increasing system size. Equilibrium finite size to large scaling identifies the $χ$ -driven transition as a second order phase transition similar to mean-field, Dicke, and Lipkin-Meshkov-Glick (LMG) models critical behaviour with the exponent of the order parameter $β\simeq 1/2$ , while the $Σ$ - and $Λ$ -driven transitions are first order. We further characterize the associated dynamical singularities through a local scaling exponent $α$ , with $α_χ\simeq 2/3$ , $α_Λ\simeq 1/3$ , and $α_Σ\simeq 3/2$ of all three parameters. The distinct scaling behaviours across the parameter channels show that dynamical criticality is not determined solely by the equilibrium order of the transition, revealing multiple dynamical scaling regimes. These non-analyticities are associated with the Fisher zeros of the Loschmidt amplitude, which cross the real time axis at critical times and the time derivatives of the return-rate function to characterize the order of DQPTs within the extended Agassi model.We investigate dynamical quantum phase transitions (DQPTs) in the extended Agassi model following sudden quenches of same level pairing ($Σ$), monopole-monopole ($χ$) and cross level pairing ($Λ$) strengths. Using exact diagonalization, we characterize the non-equilibrium dynamics through the Loschmidt echo and intensive return-rate function. Quenches across equilibrium phase boundaries produce cusp-like structures in the return rate that shows non-analyticities with increasing system size. Equilibrium finite size to large scaling identifies the $χ$-driven transition as a second order phase transition similar to mean-field, Dicke, and Lipkin-Meshkov-Glick (LMG) models critical behaviour with the exponent of the order parameter $β\simeq 1/2$, while the $Σ$- and $Λ$-driven transitions are first order. We further characterize the associated dynamical singularities through a local scaling exponent $α$, with $α_χ\simeq 2/3$, $α_Λ\simeq 1/3$, and $α_Σ\simeq 3/2$ of all three parameters. The distinct scaling behaviours across the parameter channels show that dynamical criticality is not determined solely by the equilibrium order of the transition, revealing multiple dynamical scaling regimes. These non-analyticities are associated with the Fisher zeros of the Loschmidt amplitude, which cross the real time axis at critical times and the time derivatives of the return-rate function to characterize the order of DQPTs within the extended Agassi model.

quant-pharXiv:2610.23096Oct 19, 20260 citations

Dynamical scaling behavior in non-equilibrium quantum phase transitions

Shusa Deng

Jan 1, 20110 citations

On the finite-size scaling in quantum critical phenomena

N. S. Tonchev

Physica A Statistical Mechanics and its ApplicationsFeb 1, 19915 citations

We investigate dynamical quantum phase transitions (DQPTs) in the extended Agassi model following sudden quenches of same level pairing (

Σ

), monopole-monopole (

χ

) and cross level pairing (

Λ

) strengths. Using exact diagonalization, we characterize the non-equilibrium dynamics through the Loschmidt echo and intensive return-rate function. Quenches across equilibrium phase boundaries produce cusp-like structures in the return rate that shows non-analyticities with increasing system size. Equilibrium finite size to large scaling identifies the

χ

-driven transition as a second order phase transition similar to mean-field, Dicke, and Lipkin-Meshkov-Glick (LMG) models critical behaviour with the exponent of the order parameter

β\simeq 1/2

, while the

Σ

- and

Λ

-driven transitions are first order. We further characterize the associated dynamical singularities through a local scaling exponent

α

, with

α_χ\simeq 2/3

α_Λ\simeq 1/3

, and

α_Σ\simeq 3/2

of all three parameters. The distinct scaling behaviours across the parameter channels show that dynamical criticality is not determined solely by the equilibrium order of the transition, revealing multiple dynamical scaling regimes. These non-analyticities are associated with the Fisher zeros of the Loschmidt amplitude, which cross the real time axis at critical times and the time derivatives of the return-rate function to characterize the order of DQPTs within the extended Agassi model.