伪厄米哈密顿量中的动力学量子相变：不平衡配对基塔耶夫模型
Dynamical Quantum Phase Transitions in a Pseudo-Hermitian Hamiltonian: The Imbalanced-Pairing Kitaev Model
AI总结：
研究不平衡配对基塔耶夫模型在随时间线性变化化学势下的非平衡动力学，利用动力学量子相变概念在双正交框架内分析，发现线性斜坡协议下DQPTs与实能谱有关，且非厄米性参数影响临界扫描速度。
AI中文摘要：
虽然宇称时间（PT）对称哈密顿量常与实能谱相关，但PT对称既不是实能谱的充分条件也不是必要条件。更一般地，实能谱与更广泛的伪厄米哈密顿量相关，PT对称哈密顿量是其一个简单子类。本文研究了不平衡配对基塔耶夫模型（一个典型的伪厄米系统）在随时间线性变化的化学势下的非平衡动力学。利用动力学量子相变（DQPTs）概念在双正交框架内分析动力学。结果表明，在线性斜坡协议下，仅当斜坡后的哈密顿量具有实能谱时才会发生DQPTs。对于非厄米性参数为正（γ>0）时，能谱完全为实，跨越单个量子临界点的斜坡会产生单一的临界时间族，类似于厄米情况。此外，对于跨越两个临界点或例外点的斜坡，DQPTs消失的临界扫描速度会随着非厄米性参数减小而降低，并在交错配对极限γ=-1时消失。
英文摘要：
Although parity-time (PT)-symmetric Hamiltonians are often associated with real energy spectra, PT symmetry is neither a sufficient nor a necessary condition for a real spectrum. More generally, real spectra are associated with the broader class of pseudo-Hermitian Hamiltonians, of which PT-symmetric Hamiltonians constitute a simple subclass. Here, we investigate the nonequilibrium dynamics of the imbalanced-pairing Kitaev model, a prototypical pseudo-Hermitian system, under a linearly time-dependent chemical potential. The dynamics are analyzed within the biorthogonal framework using the concept of dynamical quantum phase transitions (DQPTs). We show that, under a linear ramp protocol, DQPTs occur only when the post-ramp Hamiltonian possesses a real energy spectrum. For positive values of the non-Hermiticity parameter ($γ>0$), where the energy spectrum remains entirely real, a ramp crossing a single quantum critical point gives rise to a single family of critical times, analogous to the Hermitian case. Furthermore, for ramps crossing two critical or exceptional points, the critical sweep velocity above which DQPTs disappear decreases as the non-Hermiticity parameter is reduced and vanishes in the staggered-pairing limit, $γ=-1$.
