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A discrete “three-particle” Schrödinger operator in the Hubbard model. (English) Zbl 1177.82075
Theor. Math. Phys. 149, No. 2, 1497-1511 (2006); translation from Teor. Mat. Fiz. 149, No. 2, 228-243 (2006).
Summary: In the space \(L _{2}(T \nu \times T \nu )\), where \(T \nu \) is a \(\nu \)-dimensional torus, we study the spectral properties of the “three-particle” discrete Schrödinger operator \(\hat{H} = H_{0} + H_{1} + H_{2}\), where \(H_{0}\) is the operator of multiplication by a function and \(H_{1}\) and \(H_{2}\) are partial integral operators. We prove several theorems concerning the essential spectrum of \(\hat{H}\). We study the discrete and essential spectra of the Hamiltonians \(H^{t}\) and \(h\) arising in the Hubbard model on the three-dimensional lattice.

MSC:
82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
47B25 Linear symmetric and selfadjoint operators (unbounded)
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