Restoring canonical partition functions from imaginary chemical potential

TL;DR

This paper develops a GPU-accelerated multi-precision computational method to analyze the QCD phase transition line using the canonical approach, focusing on the properties of canonical partition functions and their temperature dependence.

Contribution

It introduces a novel GPU-based code for studying the QCD phase transition via the canonical approach, including new methods for analyzing the temperature dependence of partition functions.

Findings

Determined the crossover line in the QCD phase diagram.

Estimated the curvature parameter κ of the crossover line.

Validated the canonical approach with improved Wilson fermions on a 16^3×4 lattice.

Abstract

Using GPGPU techniques and multi-precision calculation we developed the code to study QCD phase transition line in the canonical approach. The canonical approach is a powerful tool to investigate sign problem in Lattice QCD. The central part of the canonical approach is the fugacity expansion of the grand canonical partition functions. Canonical partition functions $Z_n(T)$ are coefficients of this expansion. Using various methods we study properties of $Z_n(T)$. At the last step we perform cubic spline for temperature dependence of $Z_n(T)$ at fixed $n$ and compute baryon number susceptibility $\chi_B/T^2$ as function of temperature. After that we compute numerically $\partial\chi/ \partial T$ and restore crossover line in QCD phase diagram. We use improved Wilson fermions and Iwasaki gauge action on the $16^3 \times 4$ lattice with $m_{\pi}/m_{\rho} = 0.8$ as a sandbox to check the canonical approach. In this framework we obtain coefficient in parametrization of crossover line $T_c(\mu_B^2)=T_c\left(c-\kappa\, \mu_B^2/T_c^2\right)$ with $\kappa = -0.0453 \pm 0.0099$.