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arXiv · 1606.06631

Classification of excited-state quantum phase transitions for arbitrary number of degrees of freedom

Pavel Stránský·Pavel Cejnar
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Abstract

Classical stationary points of an analytic Hamiltonian induce singularities of the density of quantum energy levels and their flow with a control parameter in the system's infinite-size limit. We show that for a system with $f$ degrees of freedom, a non-degenerate stationary point with index $r$ causes a discontinuity (for $r$ even) or divergence ($r$ odd) of the $(f-1)$ th derivative of both density and flow of the spectrum. An increase of flatness for a degenerate stationary point shifts the singularity to lower derivatives. The findings are verified in an $f=3$ toy model.

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Pavel Stránský, Pavel Cejnar. 2016-06-21. Classification of excited-state quantum phase transitions for arbitrary number of degrees of freedom. https://doi.org/10.1016/j.physleta.2016.06.031

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