Antiferromagnetic Spin Ladders with Odd and Even number of Chains

TL;DR

This paper investigates the ground states and excitation spectra of frustrated antiferromagnetic spin ladders with varying numbers of chains, revealing differences in gap behavior between odd and even chain systems and analyzing the effects of frustration.

Contribution

It provides exact ground state solutions for certain parameter regimes and employs mean-field theory to analyze excitation spectra and spin gaps in frustrated spin ladders.

Findings

Odd m ladders are gapless; even m ladders have a gap.

Frustration increases the spin-gap magnitude.

Critical interladder coupling for gap closure is higher in frustrated systems.

Abstract

We construct frustrated antiferromagnetic spin ladders with m chains for which the exact ground state can be determined in a particular parameter regime. The excitation spectrum is shown rigorously to be gapless ( with gap ) for odd ( even ) m. In a general parameter regime, the four-chain and periodic ladders are studied using a mean-field theory based on the bond operator formalism for spin $S=1/2$. The excitation spectrum and the spin-gap are calculated in both the cases. The spin-gap of the frustrated ladder system has a larger magnitude than in the case of non-frustrated ladders. For the frustrated periodic ladder, the spin-gap vanishes at a critical value of the interladder coupling strength which is larger than the critical value in the case of non-frustrated periodic ladder.