Geodesic
On the Structure of the Essential Spectrum of a Model Many-Body Hamiltonian
Matematičeskie zametki, Tome 83 (2008) no. 1, pp. 86-94.

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In this paper, we study the essential spectrum of a model lattice Hamiltonian describing a system with fluctuating number of particles ($0\le n\le2$) in the quasimomentum representation. The spectral properties are described in terms of the boundary values of a function of a complex variable, whose meaning is that of the kernel of the Schur complement $$ H_{11}-z-H_{12}(H_{22}-z)^{-1}H_{12}^*. $$
Keywords: Schur complement, quasimomentum representation, many-body problem, fluctuating number of particles, essential spectrum. 
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T. H. Rasulov. On the Structure of the Essential Spectrum of a Model Many-Body Hamiltonian. Matematičeskie zametki, Tome 83 (2008) no. 1, pp. 86-94. http://geodesic.mathdoc.fr/item/MZM_2008_83_1_a9/

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