High Order Perturbation Theory for Spectral Densities of Multi-Particle Excitations: S=1/2 Two-Leg Heisenberg Ladder

TL;DR

This paper introduces a high order perturbation method using continuous unitary transformations to accurately compute spectral densities of multi-particle excitations, demonstrated on S=1/2 two-leg Heisenberg ladders.

Contribution

It develops a detailed perturbative approach for spectral density calculations applicable to models with identifiable elementary excitations, with technical insights and series extrapolation techniques.

Findings

Accurate spectral densities obtained for S=1/2 two-leg Heisenberg ladders.

Method effectively captures multi-particle excitation spectra.

Demonstrates the approach's applicability to complex quantum spin models.

Abstract

We present a high order perturbation approach to quantitatively calculate spectral densities in three distinct steps starting from the model Hamiltonian and the observables of interest. The approach is based on the perturbative continuous unitary transformation introduced previously. It is conceived to work particularly well in models allowing a clear identification of the elementary excitations above the ground state. These are then viewed as quasi-particles above the vacuum. The article focuses on the technical aspects and includes a discussion of series extrapolation schemes. The strength of the method is demonstrated for S=1/2 two-leg Heisenberg ladders, for which results are presented.