Effective chiral-spin Hamiltonian for odd-numbered coupled Heisenberg chains.

Abstract

An L\ifmmode\times\else\texttimes\fi{}\ensuremath{\infty} system of an odd number of coupled Heisenberg spin chains is studied using a degenerate perturbation theory, where L is the number of coupled chains. An effective chain Hamiltonian is derived explicitly in terms of two spin-1/2 degrees of freedom of a closed chain of L sites, valid in the regime where the interchain coupling is stronger than the intrachain coupling. The spin gap has been calculated numerically using the effective Hamiltonian for L=3, 5, 7, and 9 for a finite chain up to ten sites. It is suggested that the ground state of the effective Hamiltonian is correlated, by examining various variational trial states for the effective-spin chain Hamiltonian.