Restoring canonical partition functions from imaginary chemical potential

¹ School of Biomedicine, Far Eastern Federal University, Sukhanova 8, 690950 Vladivostok, Russia
² Institute for High Energy Physics NRC Kurchatov Institute, 142281 Protvino, Russia
³ School of Natural Sciences, Far Eastern Federal University, Sukhanova 8, 690950 Vladivostok, Russia
⁴ Institute of Theoretical and Experimental Physics NRC Kurchatov Institute, 117218 Moscow, Russia
⁵ Theoretical Research Division, Nishina Center, RIKEN, Wako 351-0198, Japan
⁶ Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki, Osaka, 567-0047, Japan
⁷ Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, 141700 Russia

^* Speaker, e-mail: vovagoy@gmail.com

Published online: 26 March 2018

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 χB/T² as function of temperature. After that we compute numerically ∂χ/∂T and restore crossover line in QCD phase diagram. We use improved Wilson fermions and Iwasaki gauge action on the 16³ × 4 lattice with m_π/m_ρ = 0.8 as a sandbox to check the canonical approach. In this framework we obtain coefficient in parametrization of crossover line T_c(µ²_B) = T_c(C−ĸµ²_B/T²_c) with ĸ = −0.0453 ± 0.0099.