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28 March 2024
 
  » arxiv » 1509.8429

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Semiclassical excited-state signatures of quantum phase transitions in spin chains with variable-range interactions
Manuel Gessner ; Victor Manuel Bastidas ; Tobias Brandes ; Andreas Buchleitner ;
Date 28 Sep 2015
AbstractWe 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 study spin-wave excitations around the semiclassical energy levels which reveal the quantum phase transition in their dispersion relations. These are given analytically for arbitrary numbers of spins, allowing us to discuss the relevance of the semiclassical ($Sgg 1$) and thermodynamic ($N ightarrowinfty$) limits for the quantum phase transition.
Source arXiv, 1509.8429
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