Related papers: Fourier-Matsubara series expansion for imaginary-t…
In the main part of the paper, on the basis of contour integration of complex meromorphic functions whose singularities lie onto an integration contour, in the first step, a concept of improper integrals absolute existence of meromorphic…
The calculation of imaginary time displaced correlation functions with the auxiliary field projector quantum Monte-Carlo algorithm provides valuable insight (such as spin and charge gaps) in the model under consideration. One of the authors…
We study the expansion of single-particle and two-particle imaginary-time Matsubara Green's functions of quantum impurity models in the basis of Legendre orthogonal polynomials. We discuss various applications within the dynamical…
We prove a new generalization of Davenport's Fourier expansion of the infinite series involving the fractional part function over arithmetic functions. A new Mellin transform related to the Riemann zeta function is also established.
Conceptually, the Matsubara formalism (MF), using imaginary frequencies, and the Keldysh formalism (KF), formulated in real frequencies, give equivalent results for systems in thermal equilibrium. The MF has less complexity and is thus more…
Series expansions in the chemical potential mu are studied for an effective theory of QCD which has a flux representation where the complex action is overcome. In particular we consider fugacity series, Taylor expansion and a modified…
Spontaneous symmetry breaking is responsible for rich quantum phenomena from crystalline structures to superconductivity. This concept was boldly extended to the breaking of time translation, opening an avenue to finding exotic phases of…
Based on the mathematical arguments formulated within the Multifractal Detrended Fluctuation Analysis (MFDFA) approach it is shown that in the uncorrelated time series from the Gaussian basin of attraction the effects resembling…
We formulate a new method of performing high-temperature series expansions for the spin-half Heisenberg model or, more generally, for SU($n$) Heisenberg model with arbitrary $n$. The new method is a novel extension of the well-established…
Representations for the generating functionals of static correlators of $z$-components of spins in the XY and $XX$ Heisenberg spin chains are obtained in the form of sums of the fermionic functional integrals. The peculiarity of the…
We present an expansion of a many-body correlation function in a sum of pseudomodes -- exponents with complex frequencies that encompass both decay and oscillations. The pseudomode expansion emerges in the framework of the Heisenberg…
Theoretical analysis typically involves imaginary-time correlation functions. Inferring real-time dynamical response functions from this information is notoriously difficult. However, as we articulate here, it is straightforward to compute…
Complex-valued Feynman integrals in the imaginary time formalism and zero-temperature limit suffer from particular types of infrared divergences that can not be regulated by integration dimension alone. Related problems leading to…
We put forward a functional renormalisation group approach for the direct computation of real time correlation functions, also applicable at finite temperature and density. We construct a general class of regulators that preserve the…
We illustrate how to calculate the finite-temperature linear-response conductance of quantum impurity models from the Matsubara Green function. A continued fraction expansion of the Fermi distribution is employed which was recently…
We improve on Fourier transforms (FT) between imaginary time $\tau$ and imaginary frequency $\omega_n$ used in certain quantum cluster approaches using the Hirsch-Fye method. The asymptotic behavior of the electron Green's function can be…
For a Riemann integrable function on an interval and for a point therein,we define 'Fourier series at the point on the interval' and bring out how and when the function element becomes expressible as Fourier series.In this process,we also…
The temperature-dependent Matsubara Green's function that is used to describe temperature-dependent behavior is expressed on a numerical grid. While such a grid usually has a couple of hundred points for low-energy model systems, for…
At zero temperature coupled cluster theory is widely used to predict total energies, ground state expectation values and even excited states for molecules and extended systems. Generalizations to finite temperature exist, however, they are…
We give rigorous analytical results on the temporal behavior of two-point correlation functions --also known as dynamical response functions or Green's functions-- in closed many-body quantum systems. We show that in a large class of…