Spectrum of an N-state tight-binding Hamiltonian in a Bethe lattice

By means of a canonical transformation the problem of the electronic structure in a Bethe lattice with N states per site, which normally requires a complicated numerical solution of a quadratic transfer-matrix equation, is reduced to the solution of an (N×N) eigenvalue-eigenfunction equation. The simplification achieved is considerable and great insight is obtained on the nature of the electronic spectrum by analytical means. The case N=2 is solved in its general form and the nature of the spectrum, mainly the existence of a gap and the number and location of the singularities in the density of states, is studied analytically. © 1984 The American Physical Society.

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