Finite-volume and thermodynamic-limit lower bounds for the coherently driven Bose--Hubbard model via the Lieb--Yamazaki method
Abstract
We derive rigorous lower bounds on the ground-state energy of the coherently driven Bose--Hubbard model using a Lieb--Yamazaki positive-operator decomposition. The resulting quadratic bounding Hamiltonian is diagonalized by displacement and Bogoliubov transformations, yielding explicit stability conditions and finite-volume bounds in arbitrary dimension. We establish the thermodynamic-limit energy density and characterize the excitation spectrum of the bounding Hamiltonian. We also derive its Gaussian-state observables, including filling, number fluctuations, and second-order correlations, and identify regimes of antibunching and sub-Poissonian statistics. Numerical calculations assess the tightness of the bounds across representative parameter regimes.
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BibTeX
@misc{janowicz2026finitevolume,
title = {{Finite-volume and thermodynamic-limit lower bounds for the coherently driven Bose--Hubbard model via the Lieb--Yamazaki method}},
author = {Maciej Janowicz and Joanna Kaleta and Filip Krzyżewski and Andrzej Zembrzuski},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38464},
eprint = {2610.38464},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38464},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Finite-volume and thermodynamic-limit lower bounds for the coherently driven Bose--Hubbard model via the Lieb--Yamazaki method
AU - Maciej Janowicz
AU - Joanna Kaleta
AU - Filip Krzyżewski
AU - Andrzej Zembrzuski
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38464
UR - https://arxiv.org/abs/2610.38464
AB - We derive rigorous lower bounds on the ground-state energy of the coherently driven Bose--Hubbard model using a Lieb--Yamazaki positive-operator decomposition. The resulting quadratic bounding Hamiltonian is diagonalized by displacement and Bogoliubov transformations, yielding explicit stability conditions and finite-volume bounds in arbitrary dimension. We establish the thermodynamic-limit energy density and characterize the excitation spectrum of the bounding Hamiltonian. We also derive its Gaussian-state observables, including filling, number fluctuations, and second-order correlations, and identify regimes of antibunching and sub-Poissonian statistics. Numerical calculations assess the tightness of the bounds across representative parameter regimes.
ER -