标题： 耗散动力相变作为复杂伊辛模型 显示英文标题

标题： Dissipative Dynamical Phase Transition as a Complex Ising Model

摘要： 我们研究了一种由量子比特链中局部单位演化和耗散之间的竞争引起的量子动力学相变，该链具有强的、局域的$\mathbb{Z}_2$对称性。 虽然这种演化的稳态始终是最大混合态，但我们表明，在接近这个稳态时，某些非局部可观测量的动力学行为由一个具有$\textit{complex}$横向场（cTFIM）的量子伊辛模型决定。 我们对这些可观测量进行分析，揭示了当单位演化和耗散的相对速率被调节时出现的动力学相变。 我们证明，弱耗散极限对应于一个具有大虚横向场的cTFIM，其中多体“基态”（具有最小实本征值）是无能隙的，表现出局部磁化的准长程相关性，其指数连续变化。 相应地，非局部可观测量的动力学表现出振荡行为，其振幅随时间呈指数衰减。 强耗散极限对应于cTFIM的有能隙铁磁相，而非局部可观测量在接近平衡时表现出指数衰减。 这一(1+1)维的相变具有特殊的“双侧”性质，根据从哪个相接近该相变，它可能表现为一阶或二阶相变，这一分析结果得到了数值研究的证实。 在更高维度中，我们提出了一个场论理解，说明当从cTFIM的铁磁相接近时，该相变的一阶性质，尽管具有大虚横向场的相的性质仍有待理解。 显示英文摘要

摘要： We investigate a quantum dynamical phase transition induced by the competition between local unitary evolution and dissipation in a qubit chain with a strong, on-site $\mathbb{Z}_2$ symmetry. While the steady-state of this evolution is always maximally-mixed, we show that the dynamical behavior of certain non-local observables on the approach to this steady-state is dictated by a quantum Ising model with a $\textit{complex}$ transverse-field (cTFIM). We investigate these observables analytically, uncovering a dynamical phase transition as the relative rate of unitary evolution and dissipation is tuned. We show that the weak-dissipation limit corresponds to a cTFIM with a large magnitude of the imaginary transverse-field, for which the many-body "ground-state" (with smallest real eigenvalue) is gapless, exhibiting quasi-long-range correlations of the local magnetization with a continuously-varying exponent. Correspondingly, the dynamics of the non-local observables show oscillatory behavior with an amplitude decaying exponentially in time. The strong-dissipation limit corresponds to a gapped ferromagnetic phase of the cTFIM, and non-local observables show exponential decay on the approach to equilibrium. This transition in (1+1)-dimensions has a peculiar, "two-sided" nature appearing as either first- or second-order depending on the phase from which the transition is approached, an analytic result which is corroborated by numerical studies. In higher dimensions, we present a field-theoretic understanding of the first-order nature of this transition, when approaching from the ferromagnetic phase of the cTFIM, though the nature of the phase with large imaginary transverse-field remains to be understood.