The SU(3) spin model with chemical potential by series expansion techniques
- PDF / 866,699 Bytes
- 23 Pages / 595.276 x 841.89 pts (A4) Page_size
- 36 Downloads / 151 Views
Springer
Received: July 24, Revised: September 3, Accepted: September 9, Published: October 8,
2020 2020 2020 2020
Jangho Kim,a Anh Quang Pham,a Owe Philipsena,b and Jonas Scheunerta,b a
Institut f¨ ur Theoretische Physik, Goethe-Universit¨ at Frankfurt am Main, Max-von-Laue-Str. 1, 60438 Frankfurt am Main, Germany b Helmholtz Research Academy Hesse for FAIR, Max-von-Laue-Str. 12, 60438 Frankfurt am Main, Germany
E-mail: [email protected], [email protected], [email protected], [email protected] 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 fully 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 points agree with numerical determinations to O(1%) and 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. Keywords: Effective Field Theories, Lattice Quantum Field Theory ArXiv ePrint: 2007.04187
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)051
JHEP10(2020)051
The SU(3) spin model with chemical potential by series expansion techniques
Contents 1 Introduction
1
2 The SU(3) spin model
2 4 4 5 7 10 11 12
4 The 4.1 4.2 4.3
13 13 15 17
phase transition Radius of convergence from the ratio test and Pad´e approximants The critical point Real and imaginary chemical potential
5 Conclusions
19
A Computational steps and run-times
20
1
Introduction
Despite growing demand from various fields of physics, the details of the QCD phase diagram as a function of temperature T and baryon chemical potential µB remain unknown to date. This is because of a severe sign problem due to the complex fermion determinant for µB 6= 0, which prohibits straightforward Monte Carlo simulations of lattice QCD (for introductions, see, e.g., [1, 2]). Controlled results only exist by indirect methods for the low density region µB < ∼3T , where no sign of criticality is observed [3, 4]. This has motivated the search for alternative formulations and algorithms to solve this problem. While there is a vast literature on the general subject of sign problems, all approaches devised so far work for limited classes of Hamiltonians, which do not (yet) include QCD. The purpose of the present paper is to test series expansion techniques, generically known as ‘high temperature’ expansions in the condensed matter literat
Data Loading...
