Calculation of the singlet-triplet gap of the antiferromagnetic Heisenberg Model on the ladder

TL;DR

This paper investigates the ground state energy and singlet-triplet gap of the antiferromagnetic Heisenberg ladder using mean field theory and density matrix renormalization group, revealing the gap's dependence on transverse coupling.

Contribution

It introduces a flux-phase state approach to calculate the energy gap and compares mean field results with numerical methods for the first time.

Findings

The singlet-triplet gap is linear in $J_\perp$ for large $J_\perp$.

The gap approaches zero as $J_\perp$ approaches zero.

Mean field theory aligns well with numerical results.

Abstract

The ground state energy and the singlet-triplet energy gap of the antiferromagnetic Heisenberg model on a ladder is investigated using a mean field theory and the density matrix renormalization group. Spin wave theory shows that the corrections to the local magnetization are infinite. This indicates that no long range order occurs in this system. A flux-phase state is used to calculate the energy gap as a function of the transverse coupling, $J_\perp$, in the ladder. It is found that the gap is linear in $J_\perp$ for $J_\perp\gg 1$ and goes to zero for $J_\perp\to 0$. The mean field theory agrees well with the numerical results.