Odd/Even or Half ? Entanglement Anomaly in the Bose-Hubbard model
Abstract
The area law relates the bipartite entanglement entropy of a quantum many-body ground state to the size of the boundary between the subsystems, but the geometry of this boundary is rarely discussed. We inspect this in the 1D Bose-Hubbard model at fixed density by comparing four spatial bipartitions of the periodic lattice: first half, second half, even sites, and odd sites; sharing the same number of sites but differing in how the boundary is arranged. We find analytical limits with perturbation theory: in the Mott insulator the contiguous cut obeys the area lay while the alternating cut obeys a volume law S∝ Ns, in this sense an anomaly, and for the superfluid both cuts colapse to the binomial saturation due to delocalization of the state. We formulate these limits as a statement about the many-body problem using a generalized slave-boson approach based on mean-field with quantum fluctuations while verifying with Exact Diagonalization (ED) for small lattice sizes and Densitiy Matrix Renormalization Group (DMRG) simulations for Ns≫ 1. The slave-boson Gaussian ground state allows to compute the entanglement entropy from a reduced correlation matrix for any desired bipartition consistent with ED and DMRG results. Using slave bosons the computational cost is set by the local cutoff nmax rather than the Hilbert space dimension, so we can reach lattice sizes far beyond ED. Our method is capable of establishing the partition-dependent scaling laws as a many-body feature, not only a finite-size effect, in great agreement with the ED for Ns∈[4,10] and DMRG for larger lattice sizes.
Related
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BibTeX
@misc{lopezhernandez2026oddeven,
title = {{Odd/Even or Half ? Entanglement Anomaly in the Bose-Hubbard model}},
author = {Humberto E. López-Hernández and Santiago F. Caballero-Benitez},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19884},
eprint = {2609.19884},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19884},
}
RIS
TY - UNPB
TI - Odd/Even or Half ? Entanglement Anomaly in the Bose-Hubbard model
AU - Humberto E. López-Hernández
AU - Santiago F. Caballero-Benitez
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.19884
UR - https://arxiv.org/abs/2609.19884
AB - The area law relates the bipartite entanglement entropy of a quantum many-body ground state to the size of the boundary between the subsystems, but the geometry of this boundary is rarely discussed. We inspect this in the 1D Bose-Hubbard model at fixed density by comparing four spatial bipartitions of the periodic lattice: first half, second half, even sites, and odd sites; sharing the same number of sites but differing in how the boundary is arranged. We find analytical limits with perturbation theory: in the Mott insulator the contiguous cut obeys the area lay while the alternating cut obeys a volume law S∝ N_s, in this sense an anomaly, and for the superfluid both cuts colapse to the binomial saturation due to delocalization of the state. We formulate these limits as a statement about the many-body problem using a generalized slave-boson approach based on mean-field with quantum fluctuations while verifying with Exact Diagonalization (ED) for small lattice sizes and Densitiy Matrix Renormalization Group (DMRG) simulations for N_s≫ 1. The slave-boson Gaussian ground state allows to compute the entanglement entropy from a reduced correlation matrix for any desired bipartition consistent with ED and DMRG results. Using slave bosons the computational cost is set by the local cutoff n_max rather than the Hilbert space dimension, so we can reach lattice sizes far beyond ED. Our method is capable of establishing the partition-dependent scaling laws as a many-body feature, not only a finite-size effect, in great agreement with the ED for N_s∈[4,10] and DMRG for larger lattice sizes.
ER -