Confinement in non-Abelian lattice gauge theory via persistent homology

Abstract

We investigate the structure of confining and deconfining phases in SU(2) lattice gauge theory via persistent homology, which gives us access to the topology of a hierarchy of combinatorial objects constructed from given data. Specifically, we use filtrations by traced Polyakov loops, topological densities, holonomy Lie algebra fields, as well as electric and magnetic fields. This allows for a comprehensive picture of confinement. In particular, topological densities form spatial lumps which show signatures of the classical probability distribution of instanton-dyons. Signatures of well-separated dyons located at random positions are encoded in holonomy Lie algebra fields, following the semi-classical temperature dependence of the instanton appearance probability. Debye screening discriminating between electric and magnetic fields is visible in persistent homology and pronounced at large gauge coupling. All employed constructions are gauge-invariant without a priori assumptions on the configurations under study. This work showcases the versatility of persistent homology for statistical and quantum physics studies, barely explored to date.

22 pages, 15 figures, published version

References in corpus (27)

• Learning phase transitions by confusion
• Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination
• Equivariant flow-based sampling for lattice gauge theory
• Machine Learning of Explicit Order Parameters: From the Ising Model to SU(2) Lattice Gauge Theory
• Machine Learning for Quantum Matter
• Sampling using $SU(N)$ gauge equivariant flows
• Exceptional Deconfinement in G(2) Gauge Theory
• Confining ensemble of dyons
• Discovering Symmetry Invariants and Conserved Quantities by Interpreting Siamese Neural Networks
• Lattice gauge equivariant convolutional neural networks
• An SU(2) KvBLL caloron gas model and confinement
• The Persistence of Large Scale Structures I: Primordial non-Gaussianity
• Gauge-equivariant flow models for sampling in lattice field theories with pseudofermions
• Towards Novel Insights in Lattice Field Theory with Explainable Machine Learning
• Quantitative and Interpretable Order Parameters for Phase Transitions from Persistent Homology
• Mapping distinct phase transitions to a neural network
• Topological Persistence Machine of Phase Transitions
• Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background
• Finding hidden order in spin models with persistent homology
• Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology
• Finding self-similar behavior in quantum many-body dynamics via persistent homology
• Learning quantum phase transitions through Topological Data Analysis
• Confinement and deconfinement for any gauge group from dyons viewpoint
• Finite temperature SU(2) gauge theory: critical coupling and universality class
• Persistent homology analysis of a generalized Aubry-André-Harper model
• Persistent homology analysis for dense QCD effective model with heavy quarks
• Correlating confinement to topological fluctuations near the crossover transition in QCD

Cited by in corpus (6)

• Network science Ising states of matter
• Probing universal dynamics with topological data analysis in a gluonic plasma
• Detecting defect dynamics in relativistic field theories far from equilibrium using topological data analysis
• Building imaginary-time thermal field theory with artificial neural networks
• Topological Data Analysis of Monopole Current Networks in $U(1)$ Lattice Gauge Theory
• Topological data analysis of the deconfinement transition in SU(3) lattice gauge theory