Gutzwiller Approach for Elementary Excitations in $S=1$ Antiferromagnetic Chains

TL;DR

This paper extends a Gutzwiller variational approach to study elementary excitations in $S=1$ antiferromagnetic chains, successfully calculating spectra and critical properties that align with established solutions.

Contribution

It introduces a Gutzwiller-based method for analyzing low-lying excitations in $S=1$ chains, providing results consistent with Bethe ansatz and conformal field theory.

Findings

Calculated one-magnon and two-magnon spectra match literature data.

Explained spectrum differences between Haldane and dimer phases via topology.

Obtained critical exponents and central charge consistent with theoretical predictions.

Abstract

In a previous paper [Phys. Rev. B 85,195144 (2012)], variational Monte Carlo method (based on Gutzwiller projected states) was generalized to $S=1$ systems. This method provided very good trial ground states for the gapped phases of $S=1$ bilinear-biquadratic (BLBQ) Heisenberg chain. In the present paper, we extend the approach to study the low-lying elementary excitations in $S=1$ chains. We calculate the one-magnon and two-magnon excitation spectra of the BLBQ Heisenberg chain and the results agree very well with recent data in literature. In our approach, the difference of the excitation spectrum between the Haldane phase and the dimer phase (such as the even/odd size effect) can be understood from their different topology of corresponding mean field theory. We especially study the Takhtajan-Babujian critical point. Despite the fact that the `elementary excitations' are spin-1 magnons which are different from the spin-1/2 spinons in Bethe solution, we show that the excitation spectrum, critical exponent ($\eta=0.74$) and central charge ($c=1.45$) calculated from our theory agree well with Bethe ansatz solution and conformal field theory predictions.