The SU(3) spin model with chemical potential by series expansion techniques

TL;DR

This paper uses linked cluster expansion to accurately determine the equation of state and phase structure of the SU(3) spin model with chemical potential, serving as a simplified QCD testing ground.

Contribution

It demonstrates that a 14th-order linked cluster expansion can effectively analyze the SU(3) spin model's thermodynamics and phase transitions, including at non-zero chemical potential.

Findings

Equation of state computed with ~1% accuracy

Critical end point location within ~10% of numerical results

Method applicable at various chemical potentials and effective Hamiltonians

Abstract

The $SU(3)$ spin model with chemical potential corresponds to a simplified version of QCD with static quarks in the strong coupling regime. It has been studied previously as a testing ground for new methods aiming to overcome the sign problem of lattice QCD. In this work we show that the equation of state and the phase structure of the model can be determined to reasonable accuracy by a linked cluster expansion. In particular, we compute the free energy to 14-th order in the nearest neighbour coupling. The resulting predictions for the equation of state and the location of the critical end point agree with numerical determinations to ${\cal O}(1\%)$ and ${\cal O}(10\%)$, respectively. While the accuracy for the critical couplings is still limited at the current series depth, the approach is equally applicable at zero and non-zero imaginary or real chemical potential, as well as to effective QCD Hamiltonians obtained by strong coupling and hopping expansions.