Series Expansions for Excited States of Quantum Lattice Models

TL;DR

This paper introduces a method using connected-graph expansions to generate high-order series for low-lying excited states in quantum lattice models, enabling direct calculation of excitation spectra.

Contribution

It extends existing series expansion techniques to accurately compute elementary excitation spectra in quantum many-body lattice systems.

Findings

Successfully reproduced the excitation spectrum of the transverse-field Ising chain.

Demonstrated the method's effectiveness with straightforward numerical calculations.

Provides a new tool for analyzing low-energy excitations in quantum lattice models.

Abstract

We show that by means of connected-graph expansions one can effectively generate exact high-order series expansions which are informative of low-lying excited states for quantum many-body systems defined on a lattice. In particular, the Fourier series coefficients of elementary excitation spectra are directly obtained. The numerical calculations involved are straightforward extensions of those which have already been used to calculate series expansions for ground-state correlations and $T=0$ susceptibilities in a wide variety of models. As a test, we have reproduced the known elementary excitation spectrum of the transverse-field Ising chain in its disordered phase.