Dynamical Quantum Phase Transitions in a Pseudo-Hermitian Hamiltonian: The Imbalanced-Pairing Kitaev Model

arXiv:2607.23956v1 Announce Type: new Abstract: 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 ($\gamma>0$), 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, $\gamma=-1$.

Abstract: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 ($\gamma>0$), 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, $\gamma=-1$.

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th)

arXiv:2607.23956 [quant-ph]

(or arXiv:2607.23956v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.23956 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Dynamical Quantum Phase Transitions in a Pseudo-Hermitian Hamiltonian: The Imbalanced-Pairing Kitaev Model

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