Related papers: Recent advances in the calculation of dynamical co…
State-of-the-art many-body wave function techniques rely on heuristics to achieve high accuracy at an attainable cost to solve the many-body Schr\"odinger equation. By far the most common property used to assess accuracy has been the total…
One of the challenges in using numerical methods to address many-body problems is the multi-dimensional integration over poles. More often that not, one needs such integrations to be evaluated as a function of an external variable. An…
We review the recent advances on exact results for dynamical correlation functions at large scales and related transport coefficients in interacting integrable models. We discuss Drude weights, conductivity and diffusion constants, as well…
Research on strongly correlated electron systems faces a fundamental challenge due to the complex nature of intrinsic many-body correlations. A key strategy to address this challenge lies in advancing experimental methods that can directly…
Vertex functions are a crucial ingredient of several forefront many-body algorithms in condensed matter physics. However, the full treatment of their frequency and momentum dependence severely restricts numerical calculations. A significant…
In these lecture notes, we present a pedagogical review of a number of related {\it numerically exact} approaches to quantum many-body problems. In particular, we focus on methods based on the exact diagonalization of the Hamiltonian matrix…
Driving a quantum system periodically in time can profoundly alter its long-time correlations and give rise to exotic quantum states of matter. The complexity of the combination of many-body correlations and dynamic manipulations has the…
The density matrix renormalization group (DMRG) method allows for very precise calculations of ground state properties in low-dimensional strongly correlated systems. We investigate two methods to expand the DMRG to calculations of…
We apply the functional renormalization group method to the calculation of dynamical properties of zero-dimensional interacting quantum systems. As case studies we discuss the anharmonic oscillator and the single impurity Anderson model. We…
We propose to use Ramsey interferometry and single-site addressability, available in synthetic matter such as cold atoms or trapped ions, to measure real-space and time resolved spin correlation functions. These correlation functions…
Understanding the many-body dynamics of isolated quantum systems is one of the central challenges in modern physics. To this end, the direct experimental realization of strongly correlated quantum systems allows one to gain insights into…
We demonstrate that a numerical linked cluster expansion method is a powerful tool to calculate quantum dynamics. We calculate the dynamics of the magnetization and spin correlations in the two-dimensional transverse field Ising and XXZ…
In this paper, we consider the long time asymptotics of multi-time correlation functions for quantum dynamical systems that are sufficiently random to relax to a ``reference state''. In particular, the evolution of such systems must have a…
The functional renormalization group has become a widely used tool for the analysis of the leading low-temperature correlations in weakly to moderately coupled many-fermion lattice systems. A bottleneck for quantitatively more precise…
We address the calculation of dynamical correlation functions for many fermion systems at zero temperature, using the auxiliary-field quantum Monte Carlo method. The two-dimensional Hubbard hamiltonian is used as a model system. Although…
A variational formulation for the calculation of interacting fermion systems based on the density-matrix functional theory is presented. Our formalism provides for a natural integration of explicit many-particle effects into standard…
The grand-canonical potential of many-body physics can be considered as a functional of the interaction-free correlation function. As such it obeys a nonlinear functional differential equation which can be turned into a recursion relation.…
Following the field theoretic approach of Basko et al., Ann. Phys. 321, 1126 (2006), we study in detail the real-time dynamics of a system expected to exhibit many-body localization. In particular, for time scales inaccessible to exact…
Many-body densities and correlation functions are of paramount importance for understanding quantum many-body physics. Here, we present a method to compute them; our approach is general and based on the action of bosonic or fermionic…
Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…