Related papers: Studying Hopfield models via fully lifted random d…
In this paper we look at a class of random optimization problems that arise in the forms typically known as Hopfield models. We view two scenarios which we term as the positive Hopfield form and the negative Hopfield form. For both of these…
The few determinant (FED) methodology, introduced in our previous works for 1D lattices, is here adapted for the repulsive two-dimensional Hubbard model at half-filling and with finite doping fractions. Within this configuration mixing…
[104] introduced a powerful \emph{fully lifted} (fl) statistical interpolating mechanism. It established a nested connection between blirps (bilinearly indexed random processes) and their decoupled (linearly indexed) comparative…
Bethe ansatz and bosonization procedures are used to describe the thermodynamics of the strong-coupled Hubbard chain in the \textit{spin-incoherent} Luttinger liquid (LL) regime: $J(\equiv 4t^2/U)\ll k_B T\ll E_F$, where $t$ is the hopping…
We applied renormalized singles (RS) in the multireference density functional theory (DFT) to calculate accurate energies of ground and excited states. The multireference DFT approach determines the total energy of the $N$-electron system…
We prove a large deviation principle for the finite dimensional marginals of the Gibbs distribution of the macroscopic `overlap'-parameters in the Hopfield model in the case where the number of random patterns, $M$, as a function of the…
The spherical version of the Hopfield model for pattern recognition is considered in the static limit. Structures inside the patterns are modeled by Gaussian random variables that reward correlation between pairs of spins in a given…
We present dynamical mean field theory (DMFT) results for the local spectral densities of the one- and two-particle response functions for the infinite dimensional Hubbard model in a magnetic field. We look at the different regimes…
We present evidence that learned density functional theory (``DFT'') force fields are ready for ground state catalyst discovery. Our key finding is that relaxation using forces from a learned potential yields structures with similar or…
This thesis report deals with the 1D Hubbard model and the quantum objects that diagonalize the normal ordered Hubbard hamiltonian, among those the so called PseudoFermions (PFs). These PFs have no residual energy interactions, are eta-spin…
We study the theoretical limits of the $\ell_0$ (quasi) norm based optimization algorithms when employed for solving classical compressed sensing or sparse regression problems. Considering standard contexts with deterministic signals and…
We introduce a {\em local} formalism, in terms of eigenstates of number operators, having well defined point symmetry, to solve the Hubbard model at weak coupling on a $N\times N$ square lattice (for even $N$). The key concept is that of…
The half filled Hubbard model is studied in the pair approximation of the Cluster Variation Method. The use of the $SO(4)$ symmetry of the model makes possible to give a complete analytical characterization of the ground state, by means of…
We showcase the advantages of orbital-free density-potential functional theory (DPFT), a more flexible variant of Hohenberg-Kohn density functional theory. DPFT resolves the usual trouble with the gradient-expanded kinetic energy functional…
Through a redefinition of patterns in an Hopfield-like model, we introduce and develop an approach to model discrete systems made up of many, interacting components with inner degrees of freedom. Our approach clarifies the intrinsic…
Model Hamiltonians are regularly derived from first-principles data to describe correlated matter. However, the standard methods for this contain a number of largely unexplored approximations. For a strongly correlated impurity model…
An effective low-energy model describing magnetic properties of alkali-cluster-loaded sodalites is derived by {\em ab initio} downfolding. We start with constructing an extended Hubbard model for maximally localized Wannier functions. {\em…
We propose a novel multiple testing methodology for controlling the false discovery rate (FDR) in high-dimensional linear models that integrates model-X knockoff techniques with debiased penalized regression estimators. At the foundation of…
Standard large deviation estimates or the use of the Hubbard-Stratonovich transformation reduce the analysis of the distribution of the overlap parameters essentially to that of an explicitly known random function $\Phi_{N,\b}$ on $\R^M$.…
This paper develops a general framework for controlling the false discovery rate (FDR) in multiple testing of Gaussian means against two-sided alternatives. The widely used Benjamini-Hochberg (BH) procedure provides exact FDR control under…