Entanglement-spectrum characterization of ground-state nonanalyticities in coupled excitation-phonon models

• URL: http://arxiv.org/abs/2001.11210v2
• Date: Mon, 6 Apr 2020 09:50:02 GMT
• Title: Entanglement-spectrum characterization of ground-state nonanalyticities in coupled excitation-phonon models
• Authors: Vladimir M. Stojanovic
• Abstract summary: Small-polaron transitions are analyzed through the prism of the entanglement spectrum of the excitation-phonon system. The behavior of the entanglement entropy in the vicinity of the critical excitation-phonon coupling strength chiefly originates from one specific entanglement-spectrum eigenvalue.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The polaron concept captures physical situations involving an itinerant quantum particle (excitation) that interacts strongly with bosonic degrees of freedom and becomes heavily boson-dressed. While the Gerlach-L\"{o}wen theorem rules out the occurrence of nonanalyticities of ground-state-related quantities for a broad class of polaron models, examples were found in recent years of sharp transitions pertaining to strongly momentum-dependent interactions of an excitation with dispersionless (zero-dimensional) phonons. On the example of a lattice model with Peierls-type excitation-phonon interaction, such level-crossing-type small-polaron transitions are analyzed here through the prism of the entanglement spectrum of the excitation-phonon system. By evaluating this spectrum in a numerically-exact fashion it is demonstrated that the behavior of the entanglement entropy in the vicinity of the critical excitation-phonon coupling strength chiefly originates from one specific entanglement-spectrum eigenvalue, namely the smallest one. While the discrete translational symmetry of the system implies that those eigenvalues can be labeled by the bare-excitation quasimomentum quantum numbers, here it is shown numerically that they are predominantly associated to the quasimomenta $0$ and $\pi$, including cases where a transition between the two takes place deeply in the strong-coupling regime.

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