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arXiv · 1702.05396

Complex semiclassical analysis of the Loschmidt amplitude and dynamical quantum phase transitions

Tomoyuki Obuchi·Sei Suzuki·Kazutaka Takahashi
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Abstract

We propose a new computational method of the Loschmidt amplitude in a generic spin system on the basis of the complex semiclassical analysis on the spin-coherent state path integral. We demonstrate how the dynamical transitions emerge in the time evolution of the Loschmidt amplitude for the infinite-range transverse Ising model with a longitudinal field, exposed by a quantum quench of the transverse field $Γ$ from $\infty$ or $0$. For both initial conditions, we obtain the dynamical phase diagrams that show the presence or absence of the dynamical transition in the plane of transverse field after a quantum quench and the longitudinal field. The results of semiclassical analysis are verified by numerical experiments. Experimental observation of our findings on the dynamical transition is also discussed.

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Tomoyuki Obuchi, Sei Suzuki, Kazutaka Takahashi. 2017-05-31. Complex semiclassical analysis of the Loschmidt amplitude and dynamical quantum phase transitions. https://doi.org/10.1103/physrevb.95.174305

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