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arXiv · 1905.01272

Return amplitude after a quantum quench in the XY chain

Khadijeh Najafi·M. A. Rajabpour·Jacopo Viti
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Abstract

We determine an exact formula for the transition amplitude between any two arbitrary eigenstates of the local $z$-magnetization operators in the quantum XY chain. We further use this formula to obtain an analytical expression for the return amplitude of fully polarized states and the Néel state on a ring of length $L$. Then, we investigate finite-size effects in the return amplitude: in particular quasi-particle interference halfway along the ring, a phenomenon that has been dubbed traversal~\cite{FE2016}. We show that the traversal time and the features of the return amplitude at the traversal time depend on the initial state and on the parity of $L$. Finally, we briefly discuss non-analyticities in time of the decay rates in the thermodynamic limit $L\rightarrow\infty$, which are known as dynamical phase transitions.

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Khadijeh Najafi, M. A. Rajabpour, Jacopo Viti. 2019-06-27. Return amplitude after a quantum quench in the XY chain. https://doi.org/10.1088/1742-5468%2Fab3413

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