Motion of two holes in an interacting spin background

Abstract

An antiferromagnetic spin model (S=1/2) consisting of a chain of octahedra is considered. In a certain parameter regime of the Hamiltonian the exact ground state is a local resonating-valence-bond state. We start with the t-J Hamiltonian for this model describing two holes in the same octahedron, one in the base and the other at one of the vertex sites of the octahedron. The t-J Hamiltonian consists of three parts: H_t1, describing the motion of holes along the chain, H_t2, describing the motion of holes in the bases of the octahedra, and H_J, describing the antiferromagnetic spin-spin interaction. Some exact eigenstates of H_t2 and H_J are constructed. Successive applications of H_t1 on some of these states show two types of localization for one of the holes. In one type of localization one of the holes is localized at its original location while the other hole moves. In the other type of localization, a hole, located in the base of an octahedron, cannot move away from the other hole sitting at a vertex site of the same octahedron. The localization in both cases is produced by the topology of the lattice on which the t-J model is defined.