Related papers: Truncated-Unity Parquet Equations: Application to …
We present a functional renormalization group (fRG) study of the two dimensional Hubbard model, performed with an algorithmic implementation which lifts some of the common approximations made in fRG calculations. In particular, in our fRG…
Continuous unitary transformations are a powerful tool to extract valuable information out of quantum many-body Hamiltonians, in which the so-called flow equation transforms the Hamiltonian to a diagonal or block-diagonal form in second…
We deduce a procedure to apply balanced truncation to parameter-dependent differential-algebraic systems. For that we solve multiple projected Lyapunov equations for different parameter values to compute the Gramians that are required for…
A method for solving the shell-model eigenproblem in a severely truncated space, spanned by properly selected correlated states obtained by partitioning the full configuration space, is proposed. The method describes in a practically exact…
Various perturbative and non-perturbative many-body techniques are discussed in this work. Especially, we will focus on the summation of so-called Parquet diagrams with emphasis on applications to finite nuclei. Here, the subset of two-body…
We analyze the one-dimensional extended Hubbard model with a single static impurity by using a computational technique based on the functional renormalization group. This extends previous work for spinless fermions to spin-1/2 fermions. The…
A two-particle self-consistency is rarely part of mean-field theories. It is, however, essential for avoiding spurious critical transitions and unphysical behavior. We present a general scheme for constructing analytically controllable…
Precise algorithms capable of providing controlled solutions in the presence of strong interactions are transforming the landscape of quantum many-body physics. Particularly exciting breakthroughs are enabling the computation of non-zero…
A Riemannian gradient descent algorithm and a truncated variant are presented to solve systems of phaseless equations $|Ax|^2=y$. The algorithms are developed by exploiting the inherent low rank structure of the problem based on the…
We present a highly parallelisable scheme for treating functional Renormalisation Group equations which incorporates a quasi-particle-based feedback on the flow and provides direct access to real-frequency self-energy data. This allows to…
This work is devoted to establish the strong convergence results of an iterative algorithm generated by the shrinking projection method in Hilbert spaces. The proposed approximation sequence is used to find a common element in the set of…
We present the finite-difference parquet method that greatly improves the applicability and accuracy of two-particle correlation approaches to interacting electron systems. This method incorporates the nonperturbative local physics from a…
We introduce a fast and easy-to-implement simulation algorithm for a multivariate normal distribution truncated on the intersection of a set of hyperplanes, and further generalize it to efficiently simulate random variables from a…
We address the problem of finding self-consistent parquet equations for two-body correlated Greens functions that arise out of a cumulant expansion. The general theory as developed for non-relativistic electron systems reproduces the…
A possible application of the evolution equation for the truncated Mellin moments to determination of the parton distributions in the nucleon is presented. We find that the reconstruction of the initial parton densities at scale $Q_0^2$…
The Emery model, or three-band Hubbard model, is a Hamiltonian that is thought to contain much of the physics of cuprate superconductors. This model includes two noninteracting $p$ orbitals and one interacting $d$ orbital per unit cell. Few…
The parquet equation is an exact field-theoretic equation known since the 60s that underlies numerous approximations to solve strongly correlated Fermion systems. Its derivation previously relied on combinatorial arguments classifying all…
This paper deals with (1) the truncated matrix Hamburger moment problem from the point of view of reproducing kernel Hilbert spaces of vector valued entire functions of the kind introduced and extensively studied by Louis de Branges and (2)…
The variational determination of the two-particle density matrix is an interesting, but not yet fully explored technique that allows to obtain ground-state properties of a quantum many-body system without reference to an $N$-particle wave…
We propose a novel scheme for combining efficiently the truncated-unity functional renormalization group (TUFRG) and the mean-field theory. It follows a method of Wang, Eberlein and Metzner that uses only the two-particle irreducible part…