On the structure of the essential spectrum of a model many-body Hamiltonian

Abstract

In this paper, we study the essential spectrum of a model lattice Hamiltonian describing a system with fluctuating number of particles (0 ≤ n ≤ 2) 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 $$ H_{11} - z - H_{12} \left( {H_{22} - z} \right)^{ - 1} H_{12}^ * . $$

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DOI

10.1134/s0001434608010100

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