Topological Persistence Machine of Phase Transitions

Abstract

The study of phase transitions using data-driven approaches is challenging, especially when little prior knowledge of the system is available. Topological data analysis is an emerging framework for characterizing the shape of data and has recently achieved success in detecting structural transitions in material science, such as the glass--liquid transition. However, data obtained from physical states may not have explicit shapes as structural materials. We thus propose a general framework, termed "topological persistence machine," to construct the shape of data from correlations in states, so that we can subsequently decipher phase transitions via qualitative changes in the shape. Our framework enables an effective and unified approach in phase transition analysis. We demonstrate the efficacy of the approach in detecting the Berezinskii--Kosterlitz--Thouless phase transition in the classical XY model and quantum phase transitions in the transverse Ising and Bose--Hubbard models. Interestingly, while these phase transitions have proven to be notoriously difficult to analyze using traditional methods, they can be characterized through our framework without requiring prior knowledge of the phases. Our approach is thus expected to be widely applicable and will provide practical insights for exploring the phases of experimental physical systems.

12 pages, 8 figures

References in corpus (22)

• The density-matrix renormalization group in the age of matrix product states
• Learning phase transitions by confusion
• Area laws in quantum systems: mutual information and correlations
• Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination
• Machine learning vortices at the Kosterlitz-Thouless transition
• Unsupervised machine learning and band topology
• Unsupervised machine learning account of magnetic transitions in the Hubbard model
• Unsupervised Learning of Frustrated Classical Spin Models I: Principle Component Analysis
• Phase transitions and configuration space topology
• Unsupervised Manifold Clustering of Topological Phononics
• Topological quantum phase transitions retrieved through unsupervised machine learning
• Sliced Wasserstein Kernel for Persistence Diagrams
• Scaling of the gap, fidelity susceptibility, and Bloch oscillations across the superfluid to Mott insulator transition in the one-dimensional Bose-Hubbard model
• Large-scale Monte Carlo simulation of two-dimensional classical XY model using multiple GPUs
• Evolution of Force Networks in Dense Particulate Media
• The Binder Cumulant at the Kosterlitz-Thouless Transition
• Granular Response to Impact: Topology of the Force Networks
• Unsupervised learning using topological data augmentation
• Pearson Distance is not a Distance
• Intrinsic and extrinsic geometries of correlated many-body states
• Real-Space Visualization of Quantum Phase Transition by Network Topology
• Evaluating the phase dynamics of coupled oscillators via time-variant topological features

Cited by in corpus (24)

• Measurement-induced criticality as a data-structure transition
• Quantitative and Interpretable Order Parameters for Phase Transitions from Persistent Homology
• Topological data analysis and machine learning
• Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology
• Learning quantum phase transitions through Topological Data Analysis
• Probing center vortices and deconfinement in $\mathrm{SU}(2)$ lattice gauge theory with persistent homology
• Photonic band structure design using persistent homology
• Unsupervised machine learning approaches to the $q$-state Potts model
• Persistent Homology of ${\mathbb{Z}}_2$ Gauge Theories
• Machine-learning detection of the Berezinskii-Kosterlitz-Thouless transition and the second-order phase transition in the XXZ models
• Persistent homology analysis of a generalized Aubry-André-Harper model
• Persistent homology analysis for dense QCD effective model with heavy quarks
• Persistent homology of quantum entanglement
• Persistent Homology of Fractional Gaussian Noise
• Confinement in non-Abelian lattice gauge theory via persistent homology
• Probing universal dynamics with topological data analysis in a gluonic plasma
• Network science Ising states of matter
• Dark soliton detection using persistent homology
• Detecting defect dynamics in relativistic field theories far from equilibrium using topological data analysis
• Topological Data Analysis of Monopole Current Networks in $U(1)$ Lattice Gauge Theory
• Interpretable Phase Detection and Classification with Persistent Homology
• Topological data analysis of the deconfinement transition in SU(3) lattice gauge theory
• Machine-Learning Detection of the Berezinskii-Kosterlitz-Thouless Transitions
• Structural heterogeneity: a topological characteristic to track the time evolution of soft matter systems