Complex Berry phase and imperfect non-Hermitian phase transitions
- URL: http://arxiv.org/abs/2302.02114v1
- Date: Sat, 4 Feb 2023 06:58:31 GMT
- Title: Complex Berry phase and imperfect non-Hermitian phase transitions
- Authors: Stefano Longhi and Liang Feng
- Abstract summary: spectral phase transitions from an entirely real energy spectrum to a complex spectrum can be observed in classical and quantum systems.
When the system is slowly and periodically cycled, the phase transition can become smooth, i.e. imperfect.
This is illustrated by considering the spectral phase transition of the Wannier-Stark ladders in a PT-symmetric class of two-band non-Hermitian lattices.
- Score: 6.816938564119971
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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
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