Kinetic competition controls loss-induced exceptional points of Hubbard pairs
Abstract
Two-body loss can bind two fermions in a Hubbard lattice, yet the binding threshold in the infinite lattice need not be an exceptional point (EP). At fixed total momentum K, the hops of the two particles interfere into a relative-motion hopping along each lattice direction, which sets the kinetic energy of the relative motion. On a hypercubic lattice, the threshold gc=1/[πρ2(0)] is an EP precisely when the maximum kinetic energy along one direction exceeds the sum of the transverse maxima. This dominance keeps every transverse-momentum scattering channel propagating near the band center, making the local pair Green function purely imaginary there. Two real-energy scattering zeros associated with coherent perfect absorption then coalesce at the threshold into a second-order EP of the analytically continued pair problem, where loss restores the parity-time symmetry of the pair's scattering solutions. Without a dominant direction, binding occurs without coalescence and without breaking of that symmetry. Total momentum can therefore select EP sectors even on isotropic lattices. More broadly, the kinetic structure of the two-particle continuum determines whether loss-induced binding and exceptional degeneracy coincide.
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BibTeX
@misc{tang2026kinetic,
title = {{Kinetic competition controls loss-induced exceptional points of Hubbard pairs}},
author = {Ho-Kin Tang and Xiaosen Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32123},
eprint = {2610.32123},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32123},
}
RIS
TY - UNPB
TI - Kinetic competition controls loss-induced exceptional points of Hubbard pairs
AU - Ho-Kin Tang
AU - Xiaosen Yang
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32123
UR - https://arxiv.org/abs/2610.32123
AB - Two-body loss can bind two fermions in a Hubbard lattice, yet the binding threshold in the infinite lattice need not be an exceptional point (EP). At fixed total momentum K, the hops of the two particles interfere into a relative-motion hopping along each lattice direction, which sets the kinetic energy of the relative motion. On a hypercubic lattice, the threshold g_c=1/[πρ_2(0)] is an EP precisely when the maximum kinetic energy along one direction exceeds the sum of the transverse maxima. This dominance keeps every transverse-momentum scattering channel propagating near the band center, making the local pair Green function purely imaginary there. Two real-energy scattering zeros associated with coherent perfect absorption then coalesce at the threshold into a second-order EP of the analytically continued pair problem, where loss restores the parity-time symmetry of the pair's scattering solutions. Without a dominant direction, binding occurs without coalescence and without breaking of that symmetry. Total momentum can therefore select EP sectors even on isotropic lattices. More broadly, the kinetic structure of the two-particle continuum determines whether loss-induced binding and exceptional degeneracy coincide.
ER -