Vertex corrections in the dynamic structure factor in spin ladders

TL;DR

This paper investigates how the single-triplon contribution to the dynamic structure factor in a two-leg spin ladder evolves with temperature, highlighting the dominant role of vertex corrections and validating results with experimental data.

Contribution

It combines perturbative continuous unitary transformations with mean-field calculations to quantify temperature effects on the dynamic structure factor, emphasizing the importance of vertex corrections.

Findings

Temperature diminishes one-triplon spectral weight.

Conditional excitation processes are the dominant vertex correction.

Results agree with inelastic neutron scattering experiments.

Abstract

We combine the results of perturbative continuous unitary transformations with a mean-field calculation to determine the evolution of the single-mode, i.e., one-triplon, contribution to the dynamic structure factor of a two-leg $S=1/2$ ladder on increasing temperature from zero to a finite value. The temperature dependence is induced by two effects: (i) no triplon can be excited on a rung where a thermally activated triplon is present; (ii) conditional excitation processes take place if a thermally activated triplon is present. Both effects diminish the one-triplon spectral weight upon heating. It is shown that the second effect is the dominant vertex correction in the calculation of the dynamic structure factor. The matrix elements describing the conditional triplon excitation in the two-leg Heisenberg ladder with additional four-spin ring exchange are calculated perturbatively up to order 9. The calculated results are compared to those of an inelastic neutron scattering experiment on the cuprate-ladder compound La$_{4}$Sr$_{10}$Cu$_{24}$O$_{41}$ showing convincing agreement for established values of the exchange constants.