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We present a novel treatment of finite temperature properties of the one-dimensional Hubbard model. Our approach is based on a Trotter-Suzuki mapping utilizing Shastry's classical model and a subsequent investigation of the quantum transfer…
Closed orbit theory is generalized to the semiclassical calculation of cross-correlated recurrence functions for atoms in external fields. The cross-correlation functions are inverted by a high resolution spectral analyzer to obtain the…
It is shown that there is the possibility to find at least in the perturbation framework the Matsubara theory from the $S-$matrix interpretation of the real-time finite-temperature theory if the system under consideration is in an…
Information compression plays a central role in diverse fields of modern science and technology, from communication theory to machine learning. In condensed-matter physics, the intermediate representation (IR) basis has recently been…
In this paper, we give formulas that allow one to move between transfer function type realizations of multi-variate Schur, Herglotz and Pick functions, without adding additional singularities except perhaps poles coming from the conformal…
This thesis uses Path Integrals and Green's Functions to study Gravity, Quantum Field Theory and Statistical Mechanics, particularly with respect to: finite temperature quantum systems of different spin in gravitational fields; finite…
Theoretical understanding of experimental results from relativistic heavy-ion collisions requires a microscopic approach to the behavior of QCD n-point functions at finite temperatures, as given by the hierarchy of Dyson-Schwinger…
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…
The accurate theoretical description of the dynamic properties of correlated quantum many-body systems such as the dynamic structure factor $S(\mathbf{q},\omega)$ constitutes an important task in many fields. Unfortunately, highly accurate…
The exact reduced density-matrix functional is derived from the Luttinger-Ward functional of the single-particle Green's function. Thereby, a formal link is provided between diagrammatic many-body approaches using Green's functions on the…
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…
We investigate scalar and spinor field theories in a constant magnetic field at finite temperature and chemical potential. In an external constant magnetic field the exact solution of the two-point Green functions are obtained by using the…
We compute quasi-exact \emph{ab initio} path-integral Monte Carlo results for the Matsubara Green's function of the uniform electron gas (UEG) at finite temperature over a broad range of coupling strengths ($r_s=1,\dots,10)$. This allows us…
Resummation methods using continued functions are implemented to converge divergent series appearing in perturbation problems related to continuous phase transitions in field theories. In some cases, better convergence properties are…
The many-body problem is usually approached from one of two perspectives: the first originates from an action and is based on Feynman diagrams, the second is centered around a Hamiltonian and deals with quantum states and operators. The…
Response calculations in density functional theory aim at computing the change in ground-state density induced by an external perturbation. At finite temperature these are usually performed by computing variations of orbitals, which involve…
Wave fields obeying the 2D Helmholtz equation on branched surfaces (Sommerfeld surfaces) are studied. Such surfaces appear naturally as a result of applying the reflection method to diffraction problems with straight scatterers bearing…
We use the Matsubara functional renormalization group (FRG) to describe electronic correlations within the single impurity Anderson model. In contrast to standard FRG calculations, we account for the frequency-dependence of the two-particle…
Recently, thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai, J. Chem. Phys. 136, 154104 (2012)] has been demonstrated to be an efficient and accurate electronic structure method for studying the ground-state…
In this study, we combine the ab initio Migdal-Eliashberg approach with the intermediate representation for the Green's function, enabling accurate and efficient calculations of the momentum-dependent superconducting gap function while…