Dynamic structure factor of the spin-1/2 XXZ chain in a transverse field

TL;DR

This paper presents a detailed numerical study of the dynamic structure factor of the spin-1/2 XXZ chain in a transverse field, revealing insights into its excitations and spectral properties near criticality, relevant for neutron scattering experiments.

Contribution

The study provides the first extensive MPS-based analysis of the dynamic structure factor in this model, comparing real-time evolution and Chebyshev expansion methods for efficiency and accuracy.

Findings

Longitudinal correlator is incoherent near criticality with small spectral weight.

Transverse correlator shows a dominant coherent single-particle excitation.

Spectral weight shifts with temperature, accumulating near zero wavevector.

Abstract

The spin-$\frac{1}{2}$ XXZ chain with easy-plane anisotropy in a transverse field describes well the thermodynamic properties of the material ${\rm Cs_2CoCl_4}$ in a wide range of temperatures and fields including the region close to the spin-flop Ising quantum phase transition. For a comparison with prospective inelastic neutron scattering experiments on this compound, we present results of an extensive numerical study of its dynamic structure factor $\mathcal{S}^{\alpha \beta}(k,\omega)$ using matrix-product-state (MPS) techniques. Close to criticality, the dynamic part of the correlator $\mathcal{S}^{xx}$ longitudinal to the applied field is incoherent and possesses a small total weight as the ground state is already close to saturation. The transverse correlator $\mathcal{S}^{zz}$, on the other hand, is dominated by a coherent single-particle excitation with additional spectral weight at higher energies that we tentatively attribute to a repulsively bound pair of particles. With increasing temperature, the latter quickly fades and spectral weight instead accumulates close to zero wavevector just above the single-particle energy. On a technical level, we compare the numerical efficiency of real-time evolution to an MPS-based Chebyshev expansion in the present context, finding that both methods yield results of similar quality at comparable numerical costs.