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We discuss the physics and computation of lattice QCD, a space-time lattice formulation of quantum chromodynamics, and Kenneth Wilson's seminal role in its development. We start with the fundamental issue of confinement of quarks in the…
Persistence diagrams serve as a core tool in topological data analysis, playing a crucial role in pathological monitoring, drug discovery, and materials design. However, existing quantum topological algorithms, such as the LGZ algorithm,…
Building upon the PDFSense framework developed in Ref. [1], we perform a comprehensive analysis of the sensitivity of present and future high-energy data to a number of quantities commonly evaluated in lattice gauge theory, with a…
Matter described by Quantum Chromodynamics (QCD), the theory of strong interactions, may undergo phase transitions when its temperature and the chemical potentials are varied. QCD at finite temperature is studied in the laboratory by…
A sharp stability analysis of atomistic-to-continuum coupling methods is essential for evaluating their capabilities for predicting the formation and motion of lattice defects. We formulate a simple one-dimensional model problem and give a…
Recent lattice quantum chromodynamics (lQCD) computations of bottomonium correlation functions with extended sources provide new insights into heavy-quark dynamics at distance scales which are of the order of the inverse temperature. We…
Extracting useful information from large data sets can be a daunting task. Topological methods for analyzing data sets provide a powerful technique for extracting such information. Persistent homology is a sophisticated tool for identifying…
The determination of the pattern of hadronic resonances as predicted by Quantum Chromodynamics requires the use of non-perturbative techniques. Lattice QCD has emerged as the dominant tool for such calculations, and has produced many QCD…
The effective residual interaction for a system of hadrons has a long tradition in theoretical physics. It has been mostly addressed in terms of boson exchange models. The aim of this review is to describe approaches based on lattice field…
Network theory provides various tools for investigating the structural or functional topology of many complex systems found in nature, technology and society. Nevertheless, it has recently been realised that a considerable number of systems…
Understanding associations between paired high-dimensional longitudinal datasets is a fundamental yet challenging problem that arises across scientific domains, including longitudinal multi-omic studies. The difficulty stems from the…
Lattice field theory methods, usually associated with non-perturbative studies of quantum chromodynamics, are becoming increasingly common in the calculation of ground-state and thermal properties of strongly interacting non-relativistic…
Lattice networks with dissipative interactions are often employed to analyze materials with discrete micro- or meso-structures, or for a description of heterogeneous materials which can be modelled discretely. They are, however,…
Virtual quark effects in lattice QCD are studied in an approach where the infrared modes are included in a precise and gauge-invariant manner. At fixed physical volume the required number of modes does not increase in the continuum limit,…
Predicting the mechanics of large structural networks, such as beam-based architected materials, requires a multiscale computational strategy that preserves information about the discrete structure while being applicable to large assemblies…
Topological states of matter, first discovered in quantum systems, have opened new avenues for wave manipulation beyond the quantum realm. In elastic media, realizing these topological effects requires identifying lattices that support the…
Topological quantum states are characterized by nonlocal invariants, and their detection is intrinsically challenging. Various strategies have been developed to study topological Hamiltonians through their equilibrium states. We present a…
Gauge theories are of paramount importance in our understanding of fundamental constituents of matter and their interactions. However, the complete characterization of their phase diagrams and the full understanding of non-perturbative…
We present a new method for the statistical process control of lattice structures using tools from Topological Data Analysis. Motivated by applications in additive manufacturing, such as aerospace components and biomedical implants, where…
Tensor network methods are a class of numerical tools and algorithms to study many-body quantum systems in and out of equilibrium, based on tailored variational wave functions. They have found significant applications in simulating lattice…