Investigations of QCD at non-zero isospin density

TL;DR

This paper explores the QCD phase diagram at non-zero isospin density by developing and numerically testing efficient methods to study large systems of pions, enabling analysis of up to 72 pions.

Contribution

It introduces a new, more efficient computational method for studying large multi-pion systems in QCD, extending the capability to systems of up to 72 pions.

Findings

The recursion relation reduces the computational complexity of correlation functions.

The new method allows simulation of systems with up to 72 pions.

Numerical investigations of the QCD phase diagram at non-zero isospin density.

Abstract

We investigate the QCD phase diagram as a function of isospin chemical potential at a fixed temperature by directly putting large numbers of \pi^+s into the system. Correlation functions of N \pi^+s systems involves N!N! contractions, and become extremely expensive when N is large. In order to alleviate this problem, a recursion relation of correlation functions has been derived in Ref. [1] that substantially reduces the number of independent contractions needed and makes the study of many pions systems be possible. In this proceeding this method is investigated numerically. We have also constructed a new method that is even more efficient, enabling us to study systems of up to 72 \pi^+s.