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arXiv:2607.01888

Interaction-rotation driven localization-delocalization of eigenstate in Fock space: An exact diagonalization study on trapped Bose gas

Anonymous, M. A. H. Ahsan

Published Jul 2, 2026• 0 citations
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Abstract

We investigate the localization-delocalization transition and entanglement structure in a finite system of interacting bosons in non-rotating and rotating cases. The many-body eigenspectrum is obtained via exact diagonalization within subspaces of fixed total angular momentum, and the structure of the ground state is analyzed using the inverse participation ratio (IPR), the Shannon entropy (information entropy) and the von Neumann entanglement entropy. In the non-rotating case, a transition from localized to delocalized behavior is observed with increasing interaction strength. The transition is characterized by a decrease in IPR and a corresponding increase in entropy measures, indicating spread of eigenstate weight over all the basis states in the Hilbert space. The effect becomes more pronounced with increasing number of bosons due to the increase of the Hilbert space dimension. In the presence of rotation, the system is driven further toward delocalization. For moderate angular momentum, the eigenstates exhibit partial spreading, while at higher angular momenta a saturation behavior emerges, where further increase in rotation has a limited effect on the localization properties. However, the saturation weakens with increasing system size, indicating a nontrivial interplay between rotation and number of bosons. The consistent behavior of IPR, information entropy and von Neumann entanglement entropy demonstrates that these measures provide a unified characterization of the localization-delocalization transition. The results highlight the combined role of interaction strength, rotation and number of bosons in driving the system towards delocalized state. We observe a connection between localization-delocalization and entanglement, with localized states exhibiting weaker entanglement and delocalized states showing stronger entanglement.

DOI
10.48550/arxiv.2607.01888

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We investigate the localization-delocalization transition and entanglement structure in a finite system of interacting bosons in non-rotating and rotating cases. The many-body eigenspectrum is obtained via exact diagonalization within subspaces of fixed total angular momentum, and the structure of the ground state is analyzed using the inverse participation ratio (IPR), the Shannon entropy (information entropy) and the von Neumann entanglement entropy. In the non-rotating case, a transition from localized to delocalized behavior is observed with increasing interaction strength. The transition is characterized by a decrease in IPR and a corresponding increase in entropy measures, indicating spread of eigenstate weight over all the basis states in the Hilbert space. The effect becomes more pronounced with increasing number of bosons due to the increase of the Hilbert space dimension. In the presence of rotation, the system is driven further toward delocalization. For moderate angular momentum, the eigenstates exhibit partial spreading, while at higher angular momenta a saturation behavior emerges, where further increase in rotation has a limited effect on the localization properties. However, the saturation weakens with increasing system size, indicating a nontrivial interplay between rotation and number of bosons. The consistent behavior of IPR, information entropy and von Neumann entanglement entropy demonstrates that these measures provide a unified characterization of the localization-delocalization transition. The results highlight the combined role of interaction strength, rotation and number of bosons in driving the system towards delocalized state. We observe a connection between localization-delocalization and entanglement, with localized states exhibiting weaker entanglement and delocalized states showing stronger entanglement.
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