Particle-time duality in the kicked Ising spin chain
M Akila, D Waltner, B Gutkin… - Journal of Physics A …, 2016 - iopscience.iop.org
Journal of Physics A: Mathematical and Theoretical, 2016•iopscience.iop.org
We demonstrate that the dynamics of kicked spin chains possess a remarkable duality
property. The trace of the unitary evolution operator for N spins at time T is related to one of a
non-unitary evolution operator for T spins at time N. We characterize this dual operator by its
spectrum. Using the duality relation we obtain the oscillating part of the density of states for a
large number of spins. Furthermore, the duality relation explains the anomalous short-time
behavior of the spectral form factor previously observed in the literature.
property. The trace of the unitary evolution operator for N spins at time T is related to one of a
non-unitary evolution operator for T spins at time N. We characterize this dual operator by its
spectrum. Using the duality relation we obtain the oscillating part of the density of states for a
large number of spins. Furthermore, the duality relation explains the anomalous short-time
behavior of the spectral form factor previously observed in the literature.
Abstract
We demonstrate that the dynamics of kicked spin chains possess a remarkable duality property. The trace of the unitary evolution operator for N spins at time T is related to one of a non-unitary evolution operator for T spins at time N. We characterize this dual operator by its spectrum. Using the duality relation we obtain the oscillating part of the density of states for a large number of spins. Furthermore, the duality relation explains the anomalous short-time behavior of the spectral form factor previously observed in the literature.
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