Jordan-Wigner approach to dynamic correlations in spin-ladders

TL;DR

This paper introduces a Jordan-Wigner based method combined with an extended RPA scheme to analyze dynamic correlations in low-dimensional quantum spin systems, specifically spin ladders, achieving good agreement with experimental optical conductivity data.

Contribution

The paper develops an extended Jordan-Wigner approach for spin ladders and demonstrates its effectiveness in calculating optical conductivity, including higher-order correlations.

Findings

Accurately reproduces optical conductivity of Sr2CuO3

Good agreement with experimental data for (La,Ca)14Cu24O41 along rungs

Highlights importance of higher-order correlations for leg polarization

Abstract

We present a method for studying the excitations of low-dimensional quantum spin systems based on the Jordan-Wigner transformation. Using an extended RPA-scheme we calculate the correlation function of neighboring spin flips which well approximates the optical conductivity of ${\rm Sr_2CuO_3}$. We extend this approach to the two-leg $S=1/2$--ladder by numbering the spin operators in a meander-like sequence. We obtain good agreement with the optical conductivity of the spin ladder compound (La,Ca)$_{14}$Cu$_{24}$O$_{41}$ for polarization along the rungs. For polarization along the legs higher order correlations are important to explain the weight of high-energy continuum excitations and we estimate the contribution of 4-- and 6--fermion processes.