Related papers: A Topological Data Analysis Perspective on Non-Cov…
In this paper, we give a rigorous mathematical justification for the relaxation time approximation (RTA) model. We find that only the RTA with an energy-independent relaxation time can be justified in the case of hard interactions.…
The interplay between non-trivial band topology and strong electronic correlations is a central challenge in modern condensed matter physics. We investigate this competition on a two-leg ladder model with a p-wave-like hybridisation between…
Using the tight-binding model and density functional theory, the topological invariant of the two-dimensional (2D) group III-V and IV-IV compounds are studied in the absence and the presence of an external perpendicular electric field and…
Correlations in topological states of matter provide a rich phenomenology, including a reduction in the topological classification of the interacting system compared to its non-interacting counterpart. This happens when two phases that are…
Topological Data Analysis (TDA) involves techniques of analyzing the underlying structure and connectivity of data. However, traditional methods like persistent homology can be computationally demanding, motivating the development of neural…
The importance of electronic correlation effects in the layered perovskite Sr$_2$RuO$_4$ is evidenced. To this end we use state-of-the-art LDA+DMFT (Local Density Approximation + Dynamical Mean-Field Theory) in the basis of Wannier…
The theory relevant to the study of matter in equilibrium with the radiation field is thermal quantum electrodynamics (TQED). We present a formulation of the theory, suitable for non relativistic fluids, based on a joint functional integral…
In ab initio pseudopotential calculations within density-functional theory the nonlinear exchange-correlation interaction between valence and core electrons is often treated linearly through the pseudopotential. We discuss the accuracy and…
"Concurrence topology" (Ellis and Klein \emph{Homology, Homotopy, and Applications,} \textbf{16}) is a TDA method for binary data. The idea is to construct a filtration consisting of Dowker complexes then compute persistent homology.…
The main focus of this thesis is the theoretical study of strongly interacting quantum mixtures confined in one dimension and subjected to a harmonic external potential. Such strongly correlated systems can be realized and tested in…
We explicitly build a generalized local-density approximation (GLDA) correlation functional based on one-dimensional (1D) uniform electron gases (UEGs). The fundamental parameters of the GLDA \textemdash a generalization of the widely-known…
Topological data analysis (TDA) has emerged as an effective approach in data science, with its key technique, persistent homology, rooted in algebraic topology. Although alternative approaches based on differential topology, geometric…
The ground states of the homogeneous electron gas and the homogeneous electron liquid are cornerstones in quantum physics and chemistry. They are archetypal systems in the regime of slowly varying densities in which the exchange-correlation…
The remarkable success of Deep Learning approaches is often based and demonstrated on large public datasets. However, when applying such approaches to internal, private datasets, one frequently faces challenges arising from structural…
This paper is second in the series, following Pranav et al. (2019), focused on the characterization of geometric and topological properties of 3D Gaussian random fields. We focus on the formalism of persistent homology, the mainstay of…
In this chapter, we discuss applications of topological data analysis (TDA) to spatial systems. We briefly review the recently proposed level-set construction of filtered simplicial complexes, and we then examine persistent homology in two…
We study why gold forms planar and cage-like clusters while copper and silver do not. We use density functional theory and norm-conserving pseudo-potentials with and without a scalar relativistic component. For the exchange-correlation…
Accurate bone strength prediction is essential for assessing fracture risk, particularly in aging populations and individuals with osteoporosis. Bone imaging has evolved from X-rays and DXA to clinical computed tomography (CT), and now to…
Material surface - analyte interactions play important roles in numerous processes including gas sensing. However, the effects of topological polar surface area (TPSA) of analytes on surface interactions during gas sensing have been so far…
This paper introduces topological data analysis. Starting from notions of a metric space and some elementary graph theory, we take example sets of data and demonstrate some of their topological properties. We discuss simplicial complexes…