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arXiv · 2303.10491

Two-fermion lattice Hamiltonian with first and second nearest-neighboring-site interactions

Saidakhmat N. Lakaev·Alexander K. Motovilov·Saidakbar Kh. Abdukhakimov
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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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Saidakhmat N. Lakaev, Alexander K. Motovilov, Saidakbar Kh. Abdukhakimov. 2023-03-18. Two-fermion lattice Hamiltonian with first and second nearest-neighboring-site interactions. https://doi.org/10.1088/1751-8121/ace4a6

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