Manifestation of classical bifurcation in the spectrum of the integrable quantum dimer

TL;DR

This paper investigates how classical bifurcations manifest in the quantum spectrum of an integrable dimer, revealing a connection between classical phase space structures and quantum tunneling rates.

Contribution

It demonstrates the correspondence between classical bifurcations and quantum spectral features in an integrable dimer model, combining classical analysis with quantum perturbation and numerical methods.

Findings

Classical bifurcation leads to permutational symmetry breaking trajectories.

Quantum tunneling rates reflect the classical bifurcation and separatrix.

Numerical spectra confirm classical phase space structures in the quantum regime.

Abstract

We analyze the classical and quantum properties of the integrable dimer problem. The classical version exhibits exactly one bifurcation in phase space, which gives birth to permutational symmetry broken trajectories and a separatrix. The quantum analysis yields all tunneling rates (splittings) in leading order of perturbation. In the semiclassical regime the eigenvalue spectrum obtained by numerically exact diagonalization allows to conclude about the presence of a separatrix and a bifurcation in the corresponding classical model.