Persistent homology analysis of deconfinement transition in effective Polyakov-line model
arXiv:1810.07635
Abstract
The persistent homology analysis is applied to the effective Polyakov-line model on a rectangular lattice to investigate the confinement-deconfinement nature. The lattice data are mapped onto the complex Polyakov-line plane without taking the spatial average and then the plane is divided into three domains. This study is based on previous studies for the clusters and the percolation properties in lattice QCD, but the mathematical method of the analyses are different. The spatial distribution of the data in the individual domain is analyzed by using the persistent homology to obtain information of the multiscale structure of center clusters. In the confined phase, the data in the three domains show the same topological tendency characterized by the birth and death times of the holes which are estimated via the filtration of the alpha complexes in the data space, but do not in the deconfined phase. By considering the configuration averaged ratio of the birth and death times of holes, we can construct the nonlocal order-parameter of the confinement-deconfinement transition from the multiscale topological properties of center clusters.
arXiv comment34 pages, 32 figures, manuscript revised, new figures and analyses are added
References in corpus (16)
- The Confinement Problem in Lattice Gauge Theory
- Hierarchical structures of amorphous solids characterized by persistent homology
- Persistent Homology analysis of Phase Transitions
- Comparison of complex Langevin and mean field methods applied to effective Polyakov line models
- Coherent center domains in SU(3) gluodynamics and their percolation at T_c
- Generation of confinement and other nonperturbative effects by infrared gluonic degrees of freedom
- Fractality and other properties of center domains at finite temperature Part 1: SU(3) lattice gauge theory
- Quark number holonomy and confinement-deconfinement transition
- Coherent center domains from local Polyakov loops
- Finding the effective Polyakov line action for SU(3) gauge theories at finite chemical potential
- Topological feature and phase structure of QCD at complex chemical potential
- Topological deconfinement transition in QCD at finite isospin density
- Topological Discrete Algebra, Ground State Degeneracy, and Quark Confinement in QCD
- Sign problem in -symmetric effective Polyakov-line model
- Center clusters in full QCD at finite temperature and background magnetic field
- Persistence Diagrams with Linear Machine Learning Models