Dynamical Structure Factor for the Alternating Heisenberg Chain: A Linked Cluster Calculation

TL;DR

This paper introduces a linked cluster method to accurately compute the dynamical structure factor of the alternating Heisenberg chain, revealing the dominance of two-particle states even at the uniform limit.

Contribution

The paper develops a high-order series expansion technique for calculating spectral weights of excitations in the alternating Heisenberg chain, extending understanding of spectral weight distribution.

Findings

Accurate spectral weights for one and two-particle excitations obtained.

Spectral weight dominated by two-triplet states at all bond alternation levels.

Triplet-pair excitations remain a good description even at the uniform chain limit.

Abstract

We develop a linked cluster method to calculate the spectral weights of many-particle excitations at zero temperature. The dynamical structure factor is expressed as a sum of exclusive structure factors, each representing contributions from a given set of excited states. A linked cluster technique to obtain high order series expansions for these quantities is discussed. We apply these methods to the alternating Heisenberg chain around the dimerized limit ($\lambda=0$), where complete wavevector and frequency dependent spectral weights for one and two-particle excitations (continuum and bound-states) are obtained. For small to moderate values of the inter-dimer coupling parameter $\lambda$, these lead to extremely accurate calculations of the dynamical structure factors. We also examine the variation of the relative spectral weights of one and two-particle states with bond alternation all the way up to the limit of the uniform chain ($\lambda=1$). In agreement with Schmidt and Uhrig, we find that the spectral weight is dominated by 2-triplet states even at $\lambda=1$, which implies that a description in terms of triplet-pair excitations remains a good quantitative description of the system even for the uniform chain.