论文标题
一类可集成模型的动力过渡与浴室耦合
Dynamical Transition for a class of integrable models coupled to a bath
论文作者
论文摘要
我们研究了具有平方脉冲协议的周期性驱动器，研究了$ d $尺寸的$ d尺寸积分模型的相关函数动力学。众所周知，在没有浴缸的情况下，这些模型表现出动力学相变。所有相关器衰减其稳态值为$ n_0^{ - （d+1）/2} $ [$ n_0^{ - d/d/2}] $上方[下方]一个关键频率$ω_c$，其中$ n_0 $ is $ n_0 $ is drive Cycles cycles of drive Cycles cycles cycles。我们发现，线性耦合的费米浴的存在，该浴缸维持系统的整合性可保留此过渡。我们为该系统的进化算子提供了半分析表达式，并使用它提供了一个相图，显示了不同的动力学状态作为系统浴耦合强度和浴室参数的函数。相反，当将这种模型耦合到破坏该模型的集成性的骨气浴时，我们发现相关因子的指数衰减与它们的稳态状态。我们的数值分析表明，这种指数衰减设置在上面的关键数量驱动周期$ N_C $中，这取决于系统浴耦合强度和扰动的幅度。该系统在$ N_C $以下，保留了与封闭的集成模型相同的幂律行为，并且动态过渡得以幸存。我们讨论了结果在交互式费米子系统中的适用性，并讨论了可以测试我们理论的实验。
We study the dynamics of correlation functions of a class of $d-$dimensional integrable models coupled linearly to a fermionic or bosonic bath in the presence of a periodic drive with a square pulse protocol. It is well known that in the absence of the bath, these models exhibit a dynamical phase transition; all correlators decay to their steady state values as $n_0^{-(d+1)/2}$[$n_0^{-d/2}]$ above [below] a critical frequency $ω_c$, where $n_0$ is the number of drive cycles. We find that the presence of a linearly coupled fermionic bath which maintains integrability of the system preserves this transition. We provide a semi-analytic expression for the evolution operator for this system and use it to provide a phase diagram showing the different dynamical regimes as a function of the system-bath coupling strength and the bath parameters. In contrast, when such models are coupled to a bosonic bath which breaks integrability of the model, we find exponential decay of the correlators to their steady state. Our numerical analysis shows that this exponential decay sets in above a critical number of drive cycles $n_c$ which depends on the system-bath coupling strength and the amplitude of perturbation. Below $n_c$, the system retains the power-law behavior identical to that for the closed integrable models and the dynamical transition survives. We discuss the applicability of our results for interacting fermion systems and discuss experiments which can test our theory.
