Many-body entanglement and spectral clusters in the extended hard-core bosonic Hatano-Nelson model

We study many-body entanglements and spectra of the extended bosonic Hatano-Nelson model in the hard-core limit. We show that the system undergoes a phase transition from a gapless phase to a charge density wave phase accompanied by a \(\mathcal{PT}\) transition in the first excited state. The phase...

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Bibliographic Details
Published in:arXiv.org 2024-04
Main Authors: Chao-Ze Lu, Sun, Gaoyong
Format: Article
Language:English
Subjects:
Clusters
Energy levels
Entropy
Excitation
Ground state
Phase transitions
Quantum entanglement
Scaling laws
Online Access:Get full text
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Summary:We study many-body entanglements and spectra of the extended bosonic Hatano-Nelson model in the hard-core limit. We show that the system undergoes a phase transition from a gapless phase to a charge density wave phase accompanied by a \(\mathcal{PT}\) transition in the first excited state. The phase transition is characterized by the crossing of the ground-state biorthogonal order parameter and the sudden change of the first excited-state entanglement entropy. The gapless phase is verified by the logarithmic scaling of the ground-state entanglement entropy with the central charge \(c=1\). Furthermore, we show that all energy spectral clusters would form ellipses in strong nearest-neighbor interactions, for which we establish a universal scaling law. The lengths of the major and minor axes are shown to obey power laws with respect to the nearest-neighbor interaction. The exact expressions are derived for the numbers of energy levels on the outermost elliptic ring of each clusters.
ISSN:2331-8422
DOI:10.48550/arxiv.2310.07599