Related papers: Fermionic Wave Functions from Neural-Network Const…
We design an efficient and balanced approach that captures major effects of collective electronic fluctuations in strongly correlated fermionic systems using a simple diagrammatic expansion on a basis of dynamical mean-field theory. For…
We present numerical methods to solve the Generalized Hartree-Fock theory for fermionic systems in lattices, both in thermal equilibrium and out of equilibrium. Specifically, we show how to determine the covariance matrix corresponding to…
Symmetric Hilbert spaces such as the bosonic and the fermionic Fock spaces over some `one particle space' $\K$ are formed by certain symmetrization procedures performed on the full Fock space. We investigate alternative ways of…
Divergencies appearing in perturbation expansions of interacting many-body systems can often be removed by expanding around a suitably chosen renormalized (instead of the non-interacting) Hamiltonian. We describe such a renormalized…
Representing fermionic wavefunctions efficiently is a central problem in quantum physics, chemistry and materials science. In this work, we introduce a universal and exact representation of continuous antisymmetric functions by lifting them…
Given a positive definite, bounded linear operator $A$ on the Hilbert space $\mathcal{H}_0:=l^2(E)$, we consider a reproducing kernel Hilbert space $\mathcal{H}_+$ with a reproducing kernel $A(x,y)$. Here $E$ is any countable set and…
The Dirac delta function potential is considered within the real Hilbert space approach for complex wave functions, as well as quaternionic wave functions. As has been previously determined, the real Hilbert space approach enables the…
We present an approximation scheme based on selective Hilbert space truncation for characterizing non-thermal states of magnetic systems beyond spin-wave theory. We study applications to states that are inaccessible through linear spin-wave…
In the vast majority of many-body problems, it is the kinetic energy part of the Hamiltonian that is best known microscopically, and it is the detailed form of the interactions between the particles, the potential energy term, that is…
Recordings of brain activity, such as functional MRI (fMRI), provide low-dimensional, indirect observations of neural dynamics evolving in high-dimensional, unobservable spaces. Embedding observed brain dynamics into a higher-dimensional…
We study the phase diagram of the fermionic Hubbard model on the hexagonal lattice in the space of on-site and nearest neighbor couplings with Hybrid-Monte-Carlo simulations. With pure on-site repulsion this allows to determine the critical…
Fermionic atoms in optical lattices provide a native implementation of Fermi-Hubbard (FH) models that can be used as analog quantum simulators of many-body fermionic systems. Recent experimental advances include the time-dependent local…
We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…
Variational mean field approximations tend to struggle with contemporary overparametrized deep neural networks. Where a Bayesian treatment is usually associated with high-quality predictions and uncertainties, the practical reality has been…
In this work we discuss the problem of selecting suitable approximators from families of parameterized elementary functions that are known to be dense in a Hilbert space of functions. We consider and analyze published procedures, both…
Strongly correlated electron systems are generally described by tight binding lattice Hamiltonians with strong local (on site) interactions, the most popular being the Hubbard model. Although the half filled Hubbard model can be simulated…
We present explicit expressions for the central piece of a variational method developed by Shi et al. which extends variational wave functions that are efficiently computable on classical computers beyond mean-field to generalized Gaussian…
Simulators based on neural networks offer a path to orders-of-magnitude faster electromagnetic wave simulations. Existing models, however, only address narrowly tailored classes of problems and only scale to systems of a few dozen degrees…
A scheme to form a basis and a frame for a Hilbert space of quaternion valued square integrable function from a basis and a frame, respectively, of a Hilbert space of complex valued square integrable functions is introduced. Using the…
Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional…