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

Abstract

We study the Schroedinger operators H_{λμ}(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 λ\in R and μ\in R, respectively. We establish a partition of the (λ,μ)-plane so that in each its connected component, the Schroedinger operator H_{λμ}(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_{λμ}(K) in each connected component.

arXiv comment23 pages, 3 figures

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