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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 | 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 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 | Services: | Forum | Review | PDF | Favorites |
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