Spectral Function for the S=1 Heisenberg Antiferromagetic Chain

TL;DR

This paper employs advanced DMRG techniques to compute the spectral function of the S=1 Heisenberg antiferromagnetic chain, providing precise results that validate theoretical predictions and identify the wave-vector for single particle excitation emergence.

Contribution

The study introduces improved methods for extrapolating time-dependent correlation functions in DMRG, achieving highly accurate spectral functions for the S=1 chain.

Findings

Spectral functions are computed with high precision.

Results confirm qualitative predictions of non-linear sigma models.

Critical wave-vector for excitation emergence is estimated at 0.23π-0.24π.

Abstract

We study the spectral function, $S(k,\omega)$ for the spin-1, one dimensional antiferromagnetic chain using a time-dependent density matrix renormalizaton group (DMRG) numerical method. We develop methods for extrapolating the time dependent correlation functions to larger times in order to enhance the frequency resolution. The resulting spectral functions are impressively precise and accurate. Our results confirm many qualitative expectations from non-linear $\sigma$ model methods and test them quantitatively. The critical wave-vector at which the single particle excitation emerges from the 2-particle continuum is estimated to be $0.23\pi-0.24\pi$.