Hamiltonian fingerprints of a collective mode across the BCS-BEC crossover
Abstract
Collective excitations can survive profound changes in the microscopic degrees of freedom that generate them. We track a layer-odd collective response from an exact weak-coupling hybridisation anchor into the paired regime of an attractive Hubbard bilayer and find that its Hamiltonian sensitivities evolve in a manner consistent with a crossover from single-particle interlayer hybridisation towards collective pair superexchange. At weak coupling, an exact identity for identical tunnel-coupled layers fixes a relative-phase Gaussian kernel zero at 2th, independent of the intralayer hopping. Sign-free determinant quantum Monte Carlo reveals an interaction-driven softening of the many-body spectral scale without analytic continuation, while Gaussian response theory supplies the continuous pole interpretation and shows a shift from layer-density to relative-pair-phase character. In the paired regime, the characteristic response scale acquires a growing fractional sensitivity to the intralayer hopping and an interaction dependence partway towards the 1/U law. These results show how a collective excitation can be tracked across a fermion-to-composite-boson crossover while constraining changes in its microscopic drive.
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BibTeX
@misc{prasad2026hamiltonian,
title = {{Hamiltonian fingerprints of a collective mode across the BCS-BEC crossover}},
author = {Yogeshwar Prasad},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09223},
eprint = {2609.09223},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09223},
}
RIS
TY - UNPB
TI - Hamiltonian fingerprints of a collective mode across the BCS-BEC crossover
AU - Yogeshwar Prasad
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.09223
UR - https://arxiv.org/abs/2609.09223
AB - Collective excitations can survive profound changes in the microscopic degrees of freedom that generate them. We track a layer-odd collective response from an exact weak-coupling hybridisation anchor into the paired regime of an attractive Hubbard bilayer and find that its Hamiltonian sensitivities evolve in a manner consistent with a crossover from single-particle interlayer hybridisation towards collective pair superexchange. At weak coupling, an exact identity for identical tunnel-coupled layers fixes a relative-phase Gaussian kernel zero at 2t_h, independent of the intralayer hopping. Sign-free determinant quantum Monte Carlo reveals an interaction-driven softening of the many-body spectral scale without analytic continuation, while Gaussian response theory supplies the continuous pole interpretation and shows a shift from layer-density to relative-pair-phase character. In the paired regime, the characteristic response scale acquires a growing fractional sensitivity to the intralayer hopping and an interaction dependence partway towards the 1/U law. These results show how a collective excitation can be tracked across a fermion-to-composite-boson crossover while constraining changes in its microscopic drive.
ER -