On the second-neighbor correlator in 1D XXX quantum antiferromagnetic spin chain

TL;DR

This paper calculates the ground state energy and confirms the second-neighbor correlator in a 1D XXX quantum antiferromagnetic spin chain using the asymptotic Bethe ansatz, extending previous results to variable range exchange.

Contribution

It provides a new calculation of the second-neighbor correlator for a variable range exchange model in the 1D XXX spin chain, confirming earlier results in a more general setting.

Findings

Confirmed the second-neighbor correlator value for the model.

Extended previous results to variable range exchange.

Validated the asymptotic Bethe ansatz approach.

Abstract

We have calculated the energy per site for the ground state of antiferromagnetic quantum spin chain with variable range exchange $h(j-k)\propto \sinh^2 a \sinh^{-2}a(j-k)$ in the framework of the asymptotic Bethe ansatz. By expanding it in powers of $e^{-2a}$, we have confirmed the value of the second-neighbor correlator for the model with nearest-neighbor exchange obtained earlier in the atomic limit of the Hubbard chain.