Exploring finite density QCD phase transition with canonical approach -Power of multiple precision computation-

TL;DR

This paper addresses numerical instability in finite density lattice QCD by using multiple precision calculations to accurately determine the canonical partition function, revealing pseudo phase transition lines rather than real ones.

Contribution

It introduces a multiple precision computation method to mitigate cancellation issues in the canonical approach for finite density QCD.

Findings

Multiple precision calculation reduces numerical instability.

Lee--Yang zero distribution indicates pseudo phase transition lines.

Curves in the fugacity plane are affected by significant digit variation.

Abstract

The canonical approach for finite density lattice QCD has a numerical instability. This instability makes it difficult to use the method reliably at the finite real chemical potential region. We studied this instability in detail and found that it is caused by the cancellation of significant digits. In order to reduce the effect of this cancellation, we adopt the multiple precision calculation for our discrete Fourier transformation (DFT) program, and we get the canonical partition function Zc(n,T) with required accuracy. From the obtained Zc(n,T), we calculate Lee--Yang zero distribution varying the number of significant digits. As a result, some curves surround the origin in the fugacity plane, but they are moved by varying the number of significant digits. Hence, we conclude that these curves are pseudo phase transition lines, and not real ones.