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We describe how self-adjoint ordered operator spaces, also called non-unital operator systems in the literature, can be understood as $*$-vector spaces equipped with a matrix gauge structure. We explain how this perspective has several…
We present a generalisation of the embedding space formalism to conformal field theories (CFTs) on non-trivial states and curved backgrounds, based on the ambient metric of Fefferman and Graham. The ambient metric is a Lorentzian Ricci-flat…
We establish the theoretical foundations for embedding a correlated wave function in an environment formed by Kohn-Sham orbitals. We show that introducing an approximation which equates two, in principle distinct, kinetic-energy functionals…
We propose a novel scheme to bring reduced density matrix functional theory (RDMFT) into the realm of density functional theory (DFT) that preserves the accurate density functional description at equilibrium, while incorporating accurately…
Memory function formalism or projection operator technique is an extremely useful method to study the transport and optical properties of various condensed matter systems. A recent revival of its uses in various correlated electronic…
Recently, implicit neural representations have gained popularity for learning-based 3D reconstruction. While demonstrating promising results, most implicit approaches are limited to comparably simple geometry of single objects and do not…
Density functional theory (DFT) offers a desirable balance between quantitative accuracy and computational efficiency in practical many-electron calculations. Its central component, the exchange-correlation energy functional, has been…
Tensor networks give simple representations of complex quantum states. They have proven useful in the study of condensed matter systems and conformal fields, and recently have provided toy models of AdS/CFT. Underlying the tensor network -…
The realistic description of correlated electron systems has taken an important step forward a few years ago as the combination of density functional methods and the dynamical mean-field theory was conceived. This framework allows access to…
Reduced density matrix functional theory (RDMFT) calculations are usually implemented in a decoupled manner, where the orbital and occupation optimizations are repeated alternately. Typically, orbital updates are performed using the unitary…
We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents…
Subsystem Density-Functional Theory (DFT) is an emerging technique for calculating the electronic structure of complex molecular and condensed phase systems. In this topical review, we focus on some recent advances in this field related to…
The theory of monotone operators plays a major role in modern optimization and many areas of nonlinera analysis. The central classes of monotone operators are matrices with a positive semidefinite symmetric part and subsifferential…
Diffusion models have demonstrated remarkable capabilities in synthesizing realistic images, spurring interest in using their representations for various downstream tasks. To better understand the robustness of these representations, we…
Currently, there is a growing interest in the development of a new hierarchy of methods based on the concept of seniority, which has been introduced quite recently in quantum chemistry. Despite the enormous potential of these methods, the…
We discuss some general aspects of commutators of local operators in Lorentzian CFTs, which can be obtained from a suitable analytic continuation of the Euclidean operator product expansion (OPE). Commutators only make sense as…
A new supersymmetric approach to the analysis of dynamical symmetries for matrix quantum systems is presented. Contrary to standard one dimensional quantum mechanics where there is no role for an additional symmetry due to nondegeneracy,…
We verify signatures of antiferromagnetic (AF) correlations in the double occupancy D [Gorelik et al., PRL 105, 065301 (2010)] and study their dimensional dependence using direct quantum Monte Carlo in dimensions d=2,3 and Bethe Ansatz in…
We introduce a new optimization procedure for Euclidean path integrals which compute wave functionals in conformal field theories (CFTs). We optimize the background metric in the space on which the path integration is performed.…
By employing a combined method of density functional theory and dynamical mean field theory (DFT+DMFT) we investigate the effect of electronic correlations on the magnetic and superconducting properties of the iron-based parent compound…