Topological data analysis refers to approaches for systematically and reliably computing
abstract 'shapes' of complex data sets. There are various applications of topological data …

We apply modern methods in computational topology to the task of discovering and
characterizing phase transitions. As illustrations, we apply our method to four two …

We use persistent homology and persistence images as an observable of three variants of
the two-dimensional XY model to identify and study their phase transitions. We examine …

We investigate the use of persistent homology, a tool from topological data analysis, as a
means to detect and quantitatively describe center vortices in SU (2) lattice gauge theory in …

We implement a computational pipeline based on a recent machine learning technique,
namely, topological data analysis (TDA), that has the capability of extracting powerful …

We present a new Canonical Multispin-flip Cluster Monte Carlo algorithm for Ising model
and describe efficient implementations for hybrid supercomputer. Our method takes …

We study nonequilibrium dynamics of relativistic N-component scalar field theories in
Minkowski space-time in a classical statistical regime, where typical occupation numbers of …

Observing critical phases in lattice models is challenging due to the need to analyze the
finite time or size scaling of observables. We study how the computational topology …

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 …

Topologically ordered phases of matter display a number of unique characteristics, including
ground states that can be interpreted as patterns of closed strings in the case of general Z 2 …