With open boundaries at the self-dual point, the kicked Ising model's time-evolution trace behaves as a complex Gaussian random variable consistent with circular orthogonal ensemble universality, unlike the real Gaussian for periodic boundaries.
The loschmidt spectral form factor
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Analytical study derives conditions for ergodic infinite-temperature relaxation or robust discrete time crystal subharmonic oscillations in periodically kicked spin chains, depending on kicking protocol and initial state.
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Generalized Spectral Statistics in the Kicked Ising model
With open boundaries at the self-dual point, the kicked Ising model's time-evolution trace behaves as a complex Gaussian random variable consistent with circular orthogonal ensemble universality, unlike the real Gaussian for periodic boundaries.
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Ergodic and Discrete Time Crystal Phases in Periodically Kicked Many-Body Quantum Systems: An Analytical Study
Analytical study derives conditions for ergodic infinite-temperature relaxation or robust discrete time crystal subharmonic oscillations in periodically kicked spin chains, depending on kicking protocol and initial state.