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

TL;DR

This paper derives an effective Hamiltonian for odd-numbered coupled Heisenberg spin chains in a strong inter-chain coupling regime, enabling numerical analysis of the spin gap and ground state correlations.

Contribution

It introduces a new effective Hamiltonian explicitly in terms of two spin-half degrees of freedom for odd coupled chains, valid in the strong inter-chain coupling regime.

Findings

Numerical calculation of the spin gap for L=3,5,7,9.

Evidence of correlated ground states in the effective model.

Validation of the effective Hamiltonian in the strong coupling regime.

Abstract

An $L \times \infty$ system of 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 half degrees of freedom of a closed chain of $L$ sites, valid in the regime the inter-chain coupling is stronger than the intra-chain coupling. The spin gap has been calculated numerically using the effective Hamiltonian for $L=3,5,7,9$ for a finite chain up to ten sites. It is suggested that the ground state of the effective Hamiltonian is correlated, by examining variational states for the effective chiral-spin chain Hamiltonian.