Canonical approach -- Investigation of finite density QCD phase transition

Abstract

QCD is the fundamental theory which describes the dynamics of quarks and gluons. If we understand the dynamics at finite density and temperature, i.e. QCD phase diagram and equation of states, we can progress many studies such as the studies of unstable nucleus, nuclear fusion, early universe and neutron stars. The study of QCD phase diagram is very interesting, but we have not understood it well for a long time. This is because we face a problem in this thesis at finite density. The problem is called the sign problem. It causes a decrease of the calculation accuracy. That is why we can not calculate physical quantities with high accuracy at finite chemical potential.In this thesis, we try to beat the sign problem using the 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 well at finite density. Concretely, in order to reduce the computation cost of the fermion determinant, we use the winding number expansion, in order to enhance the calculation accuracy of physical quantities, we adopt the multi precision calculation to our program based on the canonical approach. In this thesis, we will see how to improve the canonical approach and a result of thermodynamic observables which is related with the QCD phase transition at finite density.Our result shows that we do not observe the peak which represents the confinementdeconfinement phase transition in baryon number susceptibility. Therefore, we do not see the QCD phase transition yet. However, in this thesis, we find that canonical approach can explore the QCD phase diagram beyond µ B /T = 3 (µ B is the baryon chemical potential). That is, we explored the QCD phase structure beyond the validity range of Taylor expansion and reweighting method. This opens a bright window of study of QCD phase diagram at finite density. With our improvement, canonical approach has the possibility for investigation of thermodynamic observables at any chemical potential.

Anatomy of the dense QCD matter from canonical sectors

“…[28] as an example. By using the above relations and the lattice QCD data at finite µ I , we can investigate the QCD phase structure at finite µ R with certain T where the numerical error induced from the Fourier transformation can be controlled [23][24][25][26][27]. It is noted that above expression is valid even for low T and high µ R ; numerical confirmations of it in QCD effective models can be seen in Refs.…”

“…To understand the physical degree of freedom, the canonical ensembles may provide important information since they are directly related with each quark number. Therefore, we employ the canonical ensemble method [23][24][25][26][27] to discuss the QCD phase structure at moderate µ R with low T in this paper. The canonical sectors are constructed by using the imaginary chemical potential (µ I ) and then several knowledge of QCD at finite µ I play a crucial role; see Refs.…”

Roberge-Weiss periodicity, canonical sector, and modified Polyakov loop

“…In this paper, we consider the sufficiently large but finite spatial volume. This formulation is already applied to the lattice QCD [10][11][12][13][14][15] and QCD effective models [18,[23][24][25][26]. The canonical partition function, of course, obeys a canonical ensemble.…”

“…In the canonical approach [10][11][12][13][14][15], we start with the imaginary chemical potential [5,16]. This means that we can construct the canonical partition function with a fixed quark number using the grand canonical partition function at finite µ I .…”