Related papers: Diluted Generalized Random Energy Model
Generative models have advanced significantly in sampling material systems with continuous variables, such as atomistic structures. However, their application to discrete variables, like atom types or spin states, remains underexplored. In…
In view of the numerous examples in the literature it is attempted to outline a theory of Heisenberg spin systems possessing dimerized ground states (``DGS systems") which comprises all known examples. Whereas classical DGS systems can be…
We introduce a hybrid approach to applying the density matrix renormalization group (DMRG) to continuous systems, combining a grid approximation along one direction with a finite Gaussian basis set along the remaining two directions. This…
The two-electron reduced density matrix (2RDM) carries enough information to evaluate the electronic energy of a many-electron system. The variational 2RDM (v2RDM) approach seeks to determine the 2RDM directly, without knowledge of the wave…
Due to an extremely rugged structure of the free energy landscape, the determination of spin-glass ground states is among the hardest known optimization problems, found to be NP-hard in the most general case. Owing to the specific structure…
This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…
A momentum-space approach of the density-matrix renormalization-group (DMRG) method is developed. Ground state energies of the Hubbard model are evaluated using this method and compared with exact diagonalization as well as quantum…
Reduced Relativistic Gas (RRG) is a useful approach to describe the warm dark matter (WDM) or the warmness of baryonic matter in the approximation when the interaction between the particles is irrelevant. The use of Maxwell distribution…
Estimation of generalized linear mixed models (GLMMs) with non-nested random effects structures requires approximation of high-dimensional integrals. Many existing methods are tailored to the low-dimensional integrals produced by nested…
This paper describes a discrete state-space model -- and accompanying methods -- for generative modelling. This model generalises partially observed Markov decision processes to include paths as latent variables, rendering it suitable for…
Disconnectivity graphs are used to visualize the minima and the lowest energy barriers between the minima of complex systems. They give an easy and intuitive understanding of the underlying energy landscape and, as such, are excellent tools…
We present here a formulation of the electronic ground-state energy in terms of the second order reduced density matrix, using a duality argument. It is shown that the computation of the ground-state energy reduces to the search of the…
We present a unified exact tensor network approach to compute the ground state energy, identify the optimal configuration, and count the number of solutions for spin glasses. The method is based on tensor networks with the Tropical Algebra…
Machine learning is rapidly accelerating materials and chemical discovery, but most current models target energies, forces, or selected molecular properties rather than the underlying many-body electronic structure. Learning…
We present a Python implementation for RS-HDMR-GPR (Random Sampling High Dimensional Model Representation Gaussian Process Regression). The method builds representations of multivariate functions with lower-dimensional terms, either as an…
We study rough high-dimensional landscapes in which an increasingly stronger preference for a given configuration emerges. Such energy landscapes arise in glass physics and inference. In particular we focus on random Gaussian functions, and…
In this letter, we explore a generalized model based on two scenarios including the Randall-Sundrum model and Gravity model $F(T,\Theta)$. We first study the standard Randall-Sundrum Gravitational model and then add a function containing…
The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamical…
We prove that a certain discrete energy for triangulated surfaces, defined in the spirit of discrete differential geometry, converges to the Willmore energy in the sense of $\Gamma$-convergence. Variants of this discrete energy have been…
Deep neural networks are workhorse models in machine learning with multiple layers of non-linear functions composed in series. Their loss function is highly non-convex, yet empirically even gradient descent minimisation is sufficient to…