Quantum signatures of breathers in a finite Heisenberg spin chain

Abstract

A map of a quantum Heisenberg spin chain into an extended Bose–Hubbard-likeHamiltonian is set up. Within this framework, the spectrum of the correspondingBose–Hubbard chain, on a periodic one-dimensional lattice containing two, four, and sixbosons shows interesting detailed band structures. These fine structures are studied usingnumerical diagonalization, and nondegenerate and degenerate perturbation theory. We alsofocus our attention on the effect of the anisotropy and Heisenberg exchange energy on thedetailed band structures. The signature of the quantum breather is also set up bythe square of the amplitudes of the corresponding eigenvectors in real space.