Related papers: Exact downfolding and its perturbative approximati…
Accurately describing properties of challenging problems in physical sciences often requires complex mathematical models that are unmanageable to tackle head-on. Therefore, developing reduced dimensionality representations that encapsulate…
The energy spectrum of two short-range interacting particles in a harmonic potential trap has previously been related to free-space scattering phase shifts. But the existing formula for this purpose is exact only in the limit of an…
In correlated electron materials, the application of many-body techniques for the study of interaction effects or unconventional superconductivity often requires the formulation of an effective low-energy model that contains only the…
We present an accurate and efficient framework for real-space Hubbard-corrected density functional theory. In particular, we obtain expressions for the energy, atomic forces, and stress tensor suitable for real-space finite-difference…
In the present work, we start from a minimal Hamiltonian for Fermi systems where the s-wave scattering is the only low energy constant at play. Many-Body Perturbative approach that is usually valid at rather low density is first discussed.…
We apply the general principles of effective field theories to the construction of effective interactions suitable for few- and many-body calculations in a no-core shell model framework. We calculate the spectrum of systems with three and…
We give polynomial-time algorithms for the exact computation of lowest-energy (ground) states, worst margin violators, log partition functions, and marginal edge probabilities in certain binary undirected graphical models. Our approach…
A charge conserving approximation scheme determining the excitations of crystalline solids is proposed. Like other such approximations, it relies on "downfolding" of the original microscopic model to a simpler electronic model on the…
Tests of the standard model and its hypothetical extensions require precise theoretical predictions for processes involving massive, unstable particles. It is well-known that ordinary weak-coupling perturbation theory breaks down due to…
The truncation scheme dependence of the exact renormalization group equations is investigated for scalar field theories in three dimensions. The exponents are numerically estimated to the next-to-leading order of the derivative expansion.…
We examine whether essence and quantitative aspects of electronic excitation spectra are correctly captured by an effective low-energy model constructed from an {\em ab initio} downfolding scheme. A global electronic structure is first…
We develop a systematic multi-local expansion of the Polchinski-Wilson exact renormalization group (ERG) equation. Integrating out explicitly the non local interactions, we reduce the ERG equation obeyed by the full interaction functional…
This letter aims at resolving the issues raised in the recent short communication [1] and answered by [2] by proposing a systematic approximation scheme based on non-mapped shape functions, which both allows to fully exploit the unique…
The exact renormalization group (ERG) is formulated implementing the decimation of degrees of freedom by means of a particular momentum integration measure. The definition of this measure involves a distribution that links this decimation…
We study the high-dimensional linear regression problem with categorical predictors that have many levels. We propose a new estimation approach, which performs model compression via two mechanisms by simultaneously encouraging (a)…
Gaining insights from realistic dynamical models of biochemical systems can be challenging given their large number of state variables. Model reduction techniques can mitigate this by decreasing complexity by mapping the model onto a…
The physics of a quantum system with many degrees of freedom is often approximated by downfolding: most of the degrees of freedom are "folded into" a much smaller number of degrees of freedom, resulting in an effective Hamiltonian that…
The application of the exact renormalisation group to a many-fermion system with a short-range attractive force is studied. We assume a simple ansatz for the effective action with effective bosons, describing pairing effects and derive a…
Identifying the underlying models in a set of data points contaminated by noise and outliers, leads to a highly complex multi-model fitting problem. This problem can be posed as a clustering problem by the projection of higher order…
Optimization-based solvers play a central role in a wide range of signal processing and communication tasks. However, their applicability in latency-sensitive systems is limited by the sequential nature of iterative methods and the high…