Threshold Criteria for Bosonic and Fermionic Trimers on a Square Lattice: A Birman--Schwinger Comparison
Abstract
We compare two three-particle lattice models on the square lattice at total quasimomentum zero: three identical bosons with attractive contact interactions, and a two-fermion plus one distinguishable particle system with attractive interspecies contact. Using the Birman--Schwinger principle combined with symmetry reduction and strong-coupling asymptotics, we distinguish shared methodology from model-dependent spectral conclusions. For bosons, the ground-state energy behaves as minus three times the coupling plus six minus three over twice the coupling plus higher-order corrections, and exactly two bound states exist below the threshold for large coupling; the second lies at a finite distance 0.03542 below the threshold, a genuine eigenvalue rather than a threshold resonance. For fermions, the critical mass ratio is pi divided by pi minus two, approximately 2.75194; above it, a doubly degenerate level appears at strong coupling. Near onset, the binding energy follows a linear-over-logarithmic law. The results are compared with numerical finite-grid Faddeev computations and with recent three-dimensional classifications of threshold states.
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BibTeX
@misc{abdullaev2026threshold,
title = {{Threshold Criteria for Bosonic and Fermionic Trimers on a Square Lattice: A Birman--Schwinger Comparison}},
author = {Janikul Abdullaev and Abdumalik Eshniyozov and Mikhail Dolgopolov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37142},
eprint = {2610.37142},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37142},
}
RIS
TY - UNPB
TI - Threshold Criteria for Bosonic and Fermionic Trimers on a Square Lattice: A Birman--Schwinger Comparison
AU - Janikul Abdullaev
AU - Abdumalik Eshniyozov
AU - Mikhail Dolgopolov
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37142
UR - https://arxiv.org/abs/2610.37142
AB - We compare two three-particle lattice models on the square lattice at total quasimomentum zero: three identical bosons with attractive contact interactions, and a two-fermion plus one distinguishable particle system with attractive interspecies contact. Using the Birman--Schwinger principle combined with symmetry reduction and strong-coupling asymptotics, we distinguish shared methodology from model-dependent spectral conclusions. For bosons, the ground-state energy behaves as minus three times the coupling plus six minus three over twice the coupling plus higher-order corrections, and exactly two bound states exist below the threshold for large coupling; the second lies at a finite distance 0.03542 below the threshold, a genuine eigenvalue rather than a threshold resonance. For fermions, the critical mass ratio is pi divided by pi minus two, approximately 2.75194; above it, a doubly degenerate level appears at strong coupling. Near onset, the binding energy follows a linear-over-logarithmic law. The results are compared with numerical finite-grid Faddeev computations and with recent three-dimensional classifications of threshold states.
ER -