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

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 ($N\to \infty$) limit.

20 pages, 13 figures

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Cited by in corpus (13)

• Excited-state quantum phase transitions
• Particle-Time Duality in the Kicked Ising Chain I: The Dual Operator
• Particle-Time Duality in the Kicked Ising Chain II: Applications to the Spectrum
• Semiclassical Identification of Periodic Orbits in a Quantum Many-Body System
• Transition from Quantum Chaos to Localization in Spin Chains
• Multipartite-Entanglement Tomography of a Quantum Simulator
• Resolution-enhanced entanglement detection
• Long range interactions in antiferromagnetic quantum spin chains
• The local detection method: Dynamical detection of quantum discord with local operations
• Collectivity and Periodic Orbits in a Chain of Interacting, Kicked Spins
• Semiclassical bifurcations and topological phase transitions in a one-dimensional lattice of coupled Lipkin-Meshkov-Glick models
• Revealing correlations between a system and an inaccessible environment
• Multipartite entanglement in quantum phase transitions