We propose a method to find the QCD critical point at finite density calculating the canonical partition function ${\cal Z}_{\rm C} (T,N)$ by Monte-Carlo simulations of lattice QCD, and analyze data obtained by a simulation with two-flavor p4-improved staggered quarks with pion mass $m_π \approx 770 {\rm MeV}$. It is found that the shape of an effective potential changes gradually as the temperature decreases and a first order phase transition appears in the low temperature and high density region. This result strongly suggests the existence of the critical point in the $(T, μ_q)$ phase diagram.
Finite density lattice QCD without extrapolation: Bulk thermodynamics with physical quark masses from the canonical ensemble
Wuppertal University（伍珀塔尔大学）；Pennsylvania State University（宾夕法尼亚州立大学）；ELTE Eötvös Loránd University（罗兰大学）；Jülich Supercomputing Centre, Forschungszentrum Jülich（于利希超级计算中心，于利希研究中心）；Dipartimento di Fisica, Università di Torino and INFN Torino（都灵大学物理系及都灵INFN）；MTA-ELTE Lendület ”Momentum” Strongly Interacting Matter Research Group（匈牙利科学院-罗兰大学Lendulet“动量”强相互作用物质研究组）
We clarify regions where the canonical approach works well at the finite temperature and density in the Nambu-Jona-Lasinio (NJL) and Polyakov-NJL (PNJL) models. The canonical approach is a useful method for avoiding the sign problem in lattice QCD simulations at finite density, but it involves some parameters. We find that number densities computed from the canonical approach are consistent with exact values in most of the confinement phase within the parameters, which are applicable in lattice QCD.
We study the Lee-Yang zeros in the canonical approach to search phase transition points at finite temperature and density in the Nambu-Jona-Lasinio (NJL) model as an effective model of QCD. The canonical approach is a promising method to avoid the sign problem in lattice QCD at finite density. We find that a set of Lee-Yang zeros computed with finite degrees of freedom can be extrapolated to those with infinite degrees of freedom, providing the correct phase transition point. We propose the present method as a useful method for actual lattice simulations for QCD.
The study of QCD phase diagram is very interesting, but we have never understood it well. This is because we face a problem at finite density in QCD. The problem is called sign problem. It causes a decrease of the calculation accuracy. This is why, we can not calculate physical quantities accurately at finite chemical potential. In this study, we try to beat the sign problem using canonical approach of finite density lattice QCD. Although it is known that the canonical approach has several numerical problems, we can reduce them and calculate thermodynamic observables accurately at finite densi…
We discuss two new DoS approaches for finite density lattice QCD. The paper extends a recent presentation of the new techniques based on Wilson fermions, while here we now discuss and test the case of finite density QCD with staggered fermions. The first of our two approaches is based on the canonical formulation where observables at a fixed net quark number $N$ are obtained as Fourier moments of the vacuum expectation values at imaginary chemical potential $θ$. We treat the latter as densities which can be computed with the recently developed FFA method. The second approach is based on a dire…
We propose new way of heavy ion collisions experiment data analysis. We analyze physical parameters of fireball created in RHIC experiment based on Grand Canonical Distribution and different Lattice QCD data available at the moment. Our results on chemical potential are in agreement with previous model estimations and do not depend on Lattice setup. At same time, we found possible T(V) states of fireball and estimated the most probable temperature and volume of fireball as function of collision energy. We conclude that hadrom matter at RHIC experiment is thermalized and described by Grand Cano…
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 susceptibilit…
QCDLAB is a set of programs, written in GNU Octave, for lattice QCD computations. Version 2.0 includes the generation of configurations for the SU(3) theory, computation of rectangle Wilson loops as well as the low lying meson spectrum with Wilson fermions. Version 2.1 includes also the computation of the low lying meson spectrum using minimally doubled chiral fermions. In this paper, we give a brief tutorial on lattice QCD computations using QCDLAB.
This document is one of a series of whitepapers from the USQCD collaboration. Here, we outline the opportunities for, prospects of and challenges to the lattice QCD calculations relevant for the understanding of the phases and properties of hot-dense QCD matter. This program of lattice QCD calculations is relevant to current and upcoming heavy-ion experimental programs at RHIC and LHC.
This is an introductory review of lattice QCD with external fields. The study of external magnetic fields is one of the greatest achievements in modern lattice QCD. Large-scale simulations and detailed analyses have revealed intriguing properties of QCD in the magnetic fields. The study of external electric fields is more challenging because of a technical difficulty. We overview the successes and challenges of the lattice simulations with the electromagnetic fields. We also introduce a newly developing field, the lattice simulation of rotating QCD matters.
We investigate the nuclear and the quark matter at finite real chemical potential ($μ_\mathrm{R}$) and low temperature from the viewpoint of the canonical sectors constructed via the imaginary chemical potential region. Based on the large $N_\mathrm{c}$ estimation, where $N_\mathrm{c}$ is the number of color, we can discuss the confinement-deconfinement nature at finite $μ_\mathrm{R}$ from the canonical sectors. We found the expectation that the sharp change of canonical sectors at $μ_\mathrm{R} \sim M_\mathrm{B}/N_\mathrm{c}$, where $M_\mathrm{B}$ is the lowest baryon mass, is happen in the l…
