Related papers: Controllable Precision of the Projective Truncatio…
If a quantum mechanical Hamiltonian has an infinite symmetric tridiagonal (Jacobi) matrix form in some discrete Hilbert-space basis representation, then its Green's operator can be constructed in terms of a continued fraction. As an…
A comparative study of the numerical renormalization group and non-crossing approximation results for the spectral functions of the $U=\infty$ Anderson impurity model is carried out. The non-crossing approximation is the simplest conserving…
The Keldysh formalism for nonequilibrium Green's functions is a powerful theoretical framework for the description of the electronic structure, spectroscopy, and dynamics of strongly correlated systems. However, the underlying Kadanoff-Baym…
The parquet equations are a self-consistent set of equations for the effective two-particle vertex of an interacting many-fermion system. The application of these equations to bulk models is, however, demanding due to the complex emergent…
Reduced-order modeling techniques, including balanced truncation and $\mathcal{H}_2$-optimal model reduction, exploit the structure of linear dynamical systems to produce models that accurately capture the dynamics. For nonlinear systems…
The truncation and approximation errors for the set of numerical solutions computed by methods based on the algorithms of different structure are calculated and analyzed for the case of the two-dimensional steady inviscid compressible flow.…
On the basis of spin and pairing fluctuation-exchange approximation, we study the superconductivity in quasi-two-dimensional Hubbard model. The integral equations for the Green's function are self-consistently solved by numerical…
Hamiltonian Truncation Effective Theory is a framework that aims to improve the results of Hamiltonian truncation in a systematic, order-by-order fashion using Effective Field Theory methodology. The result is a truncated effective…
Reduced-order models for flows that exhibit time-periodic behavior are critical for several tasks, including active control and optimization. One well-known procedure to obtain the desired reduced-order model in the proximity of a periodic…
We present a numerical method which accurately computes the discrete spectrum and associated bound states of Hamiltonians which model electronic "edge" states localized at boundaries of one and two-dimensional crystalline materials. The…
The description of the dynamics of correlated electrons in quantum impurity models is typically described within the nonequilibrium Green function formalism combined with a suitable approximation. One common approach is based on the…
A new efficient numerical algorithm for interacting fermion systems is proposed and examined in detail. The ground state is expressed approximately by a linear combination of numerically chosen basis states in a truncated Hilbert space. Two…
The self-energy-functional approach proposed recently is applied to the single-band Hubbard model at half-filling to study the Mott-Hubbard metal-insulator transition within the most simple but non-trivial approximation. This leads to a…
Nonperturbative dynamic theory has a particular advantage in studying the transport in a quantum impurity system in a steady state. Here, we develop a new approach for obtaining the retarded Green's function expressed in resolvent form. We…
This lecture note reviews recently proposed sparse-modeling approaches for efficient ab initio many-body calculations based on the data compression of Green's functions. The sparse-modeling techniques are based on a compact orthogonal…
This paper presents data-driven implementations of balanced truncation and several of its generalizations that rely exclusively on transfer function samples on the imaginary axis. Rather than implicitly approximating the Gramians via…
We demonstrate the efficiency of a recent exact-gradient optimal control methodology by applying it to a challenging many-body problem, crossing the superfluid to Mott-insulator phase transition in the Bose-Hubbard model. The system size…
Estimating truncated density models is difficult, as these models have intractable normalising constants and hard to satisfy boundary conditions. Score matching can be adapted to solve the truncated density estimation problem, but requires…
Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…
We treat the two-particle Green's function in the Hubbard model using the recently developed tau-CPA, a hybrid treatment that applies the coherent-potential approximation (CPA) up to a time tau related to the inverse of the band width,…