Longitudinal excitations in quantum antiferromagnets

TL;DR

This paper investigates the longitudinal excitations in low-dimensional quantum antiferromagnets using a microscopic many-body approach, revealing energy gaps related to long-range order and comparing results with experimental data.

Contribution

It extends magnon-density-wave theory to low dimensions and provides a detailed energy spectrum of longitudinal modes in quasi-1D and 2D Heisenberg antiferromagnets.

Findings

Longitudinal mode has a non-zero energy gap with long-range order.

Gap becomes zero in the pure 1D isotropic model.

Numerical gap matches experimental observations in KCuF3.

Abstract

By extending our recently proposed magnon-density-waves to low dimensions, we investigate, using a microscopic many-body approach, the longitudinal excitations of the quasi-one-dimensional (quasi-1d) and quasi-2d Heisenberg antiferromagnetic systems on a bipartite lattice with a general spin quantum number. We obtain the full energy spectrum of the longitudinal mode as a function of the coupling constants in the original lattice Hamiltonian and find that it always has a non-zero energy gap if the ground state has a long-range order and becomes gapless for the pure isotropic 1d model. The numerical value of the minimum gap in our approximation agrees with that of a longitudinal mode observed in the quasi-1d antiferromagnetic compound KCuF${}_3$ at low temperature. It will be interesting to compare values of the energy spectrum at other momenta if their experimental results are available.