Semiclassical excited-state signatures of quantum phase transitions in spin chains with variable-range interactions

TL;DR

This paper explores the excitation spectrum of variable-range spin chains with arbitrary spin, revealing how semiclassical methods can predict quantum phase transitions and bifurcations, bridging classical and quantum descriptions.

Contribution

It introduces a semiclassical framework for analyzing excitation spectra and quantum bifurcations in spin chains with variable interactions and arbitrary spin S.

Findings

Semiclassical energy manifolds determine quantum spectra.

Bifurcations in energy landscapes signal phase transitions.

Analytic dispersion relations for spin-wave excitations.

Abstract

We study the excitation spectrum of a family of transverse-field spin chain models with variable interaction range and arbitrary spin $S$, which in the case of $S=1/2$ interpolates between the Lipkin-Meshkov-Glick and the Ising model. For any finite number $N$ of spins, a semiclassical energy manifold is derived in the large-$S$ limit employing bosonization methods, and its geometry is shown to determine not only the leading-order term but also the higher-order quantum fluctuations. Based on a multi-configurational mean-field ansatz, we obtain the semiclassical backbone of the quantum spectrum through the extremal points of a series of one-dimensional energy landscapes -- each one exhibiting a bifurcation when the external magnetic field drops below a threshold value. The obtained spectra become exact in the limit of vanishing or very strong external, transverse magnetic fields. Further analysis of the higher-order corrections in $1/\sqrt{2S}$ enables us to analytically study the dispersion relations of spin-wave excitations around the semiclassical energy levels. Within the same model, we are able to investigate quantum bifurcations, which occur in the semiclassical ($S\gg 1$) limit, and quantum phase transitions, which are observed in the thermodynamic ($N\rightarrow\infty$) limit.