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-Löwen 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 with the quasimomenta 0 and , including cases where a transition between the two takes place deeply in the strong-coupling regime.
- Received 3 January 2020
- Revised 10 February 2020
- Accepted 16 March 2020
DOI:https://doi.org/10.1103/PhysRevB.101.134301
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