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We perform a data-driven dimensionality reduction of the scale-dependent 4-point vertex function characterizing the functional Renormalization Group (fRG) flow for the widely studied two-dimensional $t - t'$ Hubbard model on the square…
We analyze the one-dimensional (1D) and the two-dimensional (2D) repulsive Hubbard models (HM) for densities slightly away from half-filling through the behavior of two central quantities of a system: the uniform charge and spin…
A method for finding reduced-order approximations of turbulent flow models is presented. The method preserves bounds on the production of turbulent energy in the sense of the $\curly{L}_2$ norm of perturbations from a notional laminar…
We introduce a diagrammatic multi-scale approach to the Hubbard model based on the interaction-irreducible (multi-boson) vertex of a small cluster embedded in a self-consistent medium. The vertex captures short-ranged correlations up to the…
In this work, we analyze the Born, Bogoliubov, Green, Kirkwood and Yvon (BBGKY) hierarchy of equations for describing the full time-evolution of a many-body fermionic system in terms of its reduced density matrices (at all orders). We…
In the search for accurate approximate solutions of the many-body Schr\"odinger equation, reduced density matrices play an important role, as they allow to formulate approximate methods with polynomial scaling in the number of particles.…
Bilevel optimization has been recently revisited for designing and analyzing algorithms in hyperparameter tuning and meta learning tasks. However, due to its nested structure, evaluating exact gradients for high-dimensional problems is…
We analyze a variety of integration schemes for the momentum space functional renormalization group calculation with the goal of finding an optimized scheme. Using the square lattice $t-t'$ Hubbard model as a testbed we define and benchmark…
In this work, we introduce an original self-consistent scheme based on the one-body reduced density matrix ($\gamma$) formalism. A significant feature of this methodology is the utilization of an optimal unitary transformation of the…
The main goal of this paper is to reconsider a phenomenon which was treated in earlier work of the authors' on several truncated matricial moment problems. Using a special kind of Schur complement we obtain a more transparent insight into…
We consider the low-energy particle-particle scattering properties in a periodic simple cubic crystal. In particular, we investigate the relation between the two-body scattering length and the energy shift experienced by the lowest-lying…
This paper introduces a novel ansatz-based technique for solution of the Hubbard model over two length scales. Short range correlations are treated exactly using a dynamical cluster approximation QMC simulation, while longer-length-scale…
We consider a class of adaptive multilevel domain decomposition-like algorithms, built from a combination of adaptive multilevel finite element, domain decomposition, and partition of unity methods. These algorithms have several interesting…
The development of numerical methods capable of simulating realistic materials with strongly correlated electrons, with controllable errors, is a central challenge in quantum many-body physics. Here we describe how a hybrid between…
Ground state properties of the Hubbard model on a two-dimensional square lattice are studied by the auxiliary-field quantum Monte Carlo method. Accurate results for energy, double occupancy, effective hopping, magnetization, and momentum…
In this thesis the variational optimisation of the density matrix is discussed as a method in many-body quantum mechanics. This is a relatively unknown technique in which one tries to obtain the two-particle reduced density matrix directly…
We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…
The second-order reduced density matrix method (the RDM method) has performed well in determining energies and properties of atomic and molecular systems, achieving coupled-cluster singles and doubles with perturbative triples (CC SD(T))…
An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the…
Randomized matrix compression techniques, such as the Johnson-Lindenstrauss transform, have emerged as an effective and practical way for solving large-scale problems efficiently. With a focus on computational efficiency, however, forsaking…