Spin Excitation Spectra of Anisotropic Spin-$1/2$ Triangular Lattice Heisenberg Antiferromagnets

TL;DR

This paper uses advanced tensor network methods to compute the spin excitation spectra of a highly frustrated quantum antiferromagnet, providing detailed insights that align with experimental neutron scattering data and predicting new observable features.

Contribution

First comprehensive numerical analysis of dynamical spectra in the anisotropic spin-1/2 triangular Heisenberg model using tensor network techniques.

Findings

Reproduces key features of neutron scattering spectra in Ba3CoSb2O9

Identifies longitudinal Higgs modes at intermediate energies

Spectral features are weakly affected by anisotropy ratio

Abstract

Investigation of dynamical excitations is difficult but crucial to the understanding of many exotic quantum phenomena discovered in quantum materials. This is particularly true for highly frustrated quantum antiferromagnets whose dynamical properties deviate strongly from theoretical predictions made based on the spin-wave or other approximations. Here we present a large-scale numerical calculation on the dynamical correlation functions of spin-$1/2$ triangular Heisenberg model using a state-of-the-art tensor network renormalization group method. The calculated results allow us to gain for the first time a comprehensive picture on the nature of spin excitation spectra in this highly frustrated quantum system. It provides a quantitative account for all the key features of the dynamical spectra disclosed by inelastic neutron scattering measurements for $\rm Ba_3CoSb_2O_9$, revealing the importance of the interplay between low- and high-energy excitations and its renormalization effect to the low-energy magnon bands and high-energy continuums. We identify the longitudinal Higgs modes in the intermediate-energy scale and predict the energy and momentum dependence of spectral functions along the three principal axes that can be verified by polarized neutron scattering experiments. Furthermore, we find that the spin excitation spectra weakly depend on the anisotropic ratio of the antiferromagnetic interaction.