The first Schur complement for a lattice spin-boson model with at most two photons
Tulkin H. RasulovBukhara State University, Bukhara branch of the Institute of Mathematics named after V. I. Romanovskiy, Bukhara, UzbekistanElyor B. DilmurodovBukhara State University, Bukhara branch of the Institute of Mathematics named after V. I. Romanovskiy, Bukhara, Uzbekistan
ABI
Abstract
In the present paper, we consider a lattice spin-boson model A 2 with a fixed atom and at most two photons. We construct the first Schur complement S 1 () with spectral parameter corresponding to A 2 . We prove the Birman-Schwinger principle for A 2 with respect to S 1 (). We investigate an important properties of S 1 () related to the number of eigenvalues of A 2 for all dimensions d of the torus T d and for any coupling constant > 0.
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