Two-fermion lattice Hamiltonian with first and second
nearest-neighboring-site interactions
- URL: http://arxiv.org/abs/2303.10491v2
- Date: Tue, 18 Jul 2023 11:43:08 GMT
- Title: Two-fermion lattice Hamiltonian with first and second
nearest-neighboring-site interactions
- Authors: Saidakhmat N. Lakaev, Alexander K. Motovilov, Saidakbar Kh.
Abdukhakimov
- Abstract summary: We study the Schroedinger operators H_lambdamu(K), with K in T, the fixed quasi-momentum of the particles pair.
We establish a sharp lower bound for the number of isolated eigenvalues of H_lambdamu(K) in each connected component.
- Score: 68.8204255655161
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We study the Schroedinger operators H_{\lambda\mu}(K), with K \in T_2 the
fixed quasi-momentum of the particles pair, associated with a system of two
identical fermions on the two-dimensional lattice Z_2 with first and second
nearest-neighboring-site interactions of magnitudes \lambda \in R and \mu \in
R, respectively. We establish a partition of the (\lambda,\mu)-plane so that in
each its connected component, the Schroedinger operator H_{\lambda\mu}(0) has a
definite (fixed) number of eigenvalues, which are situated below the bottom of
the essential spectrum and above its top. Moreover, we establish a sharp lower
bound for the number of isolated eigenvalues of H_{\lambda\mu}(K) in each
connected component.
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