Complex Berry phase and imperfect non-Hermitian phase transitions
Complex Berry phase and imperfect non-Hermitian phase transitions
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DOI：
10.1103/physrevb.107.085122
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发表时间：
2023-02
影响因子：
3.7
通讯作者：
S. Longhi;Liang Feng
中科院分区：
文献类型：
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作者：
S. Longhi;Liang Feng
在由有效非厄米哈密顿量描述的许多经典和量子系统中，当系统中的非厄米参数增加到临界值以上时，可以观察到从完全真实的能谱到复能谱的谱相变。一个典型的例子是由具有宇称时间（PT）对称性的系统，其中的能量谱保持完全真实的在不间断的PT阶段，而过渡到复杂的能量被观察到在不间断的PT阶段。这样的光谱相变是普遍尖锐的。然而，当系统缓慢地周期性循环时，由于与系统的循环绝热演化相关联的复杂Berry相，相变可以变得平滑，即不完美。这一显著的现象是通过考虑一个PT对称类的两带非厄米晶格中的Wannier-Stark阶梯的光谱相变来说明的，受到外部直流场的影响，揭示了Zak相位的非零虚部--由整个布里渊区演化的布洛赫本征态拾取的Berry相位--是造成不完美光谱相变的原因
In many classical and quantum systems described by an effective non-Hermitian Hamiltonian, spectral phase transitions, from an entirely real energy spectrum to a complex spectrum, can be observed as a non-Hermitian parameter in the system is increased above a critical value. A paradigmatic example is provided by systems possessing parity-time (PT) symmetry, where the energy spectrum remains entirely real in the unbroken PT phase while a transition to complex energies is observed in the unbroken PT phase. Such spectral phase transitions are universally sharp. However, when the system is slowly and periodically cycled, the phase transition can become smooth, i.e. imperfect, owing to the complex Berry phase associated to the cyclic adiabatic evolution of the system. This remarkable phenomenon is illustrated by considering the spectral phase transition of the Wannier-Stark ladders in a PT-symmetric class of two-band non-Hermitian lattices subjected to an external dc field, unraveling that a non-vanishing imaginary part of the Zak phase -- the Berry phase picked up by a Bloch eigenstate evolving across the entire Brillouin zone -- is responsible for imperfect spectral phase transitions