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

TL;DR

This paper links classical stationary points of Hamiltonians to singularities in quantum energy level densities, revealing how these points cause specific discontinuities or divergences in spectral derivatives, with verification in a three-degree-of-freedom model.

Contribution

It generalizes the connection between classical stationary points and quantum spectral singularities to systems with arbitrary degrees of freedom.

Findings

Non-degenerate stationary points cause derivative discontinuities or divergences in spectra.

Degenerate stationary points shift singularities to lower derivatives.

Verification performed in a three-degree-of-freedom toy model.

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.