Related papers: Non-perturbative conserving approximations and Lut…
A self-energy-functional approach is applied to construct cluster approximations for correlated lattice models. It turns out that the cluster-perturbation theory (Senechal et al, PRL 84, 522 (2000)) and the cellular dynamical mean-field…
A strictly truncated (weak-coupling) perturbation theory is applied to the attractive Holstein and Hubbard models in infinite dimensions. These results are qualified by comparison with essentially exact Monte Carlo results. The second order…
We develop a Liouville perturbation theory for weakly driven and weakly open quantum systems in situations when the unperturbed system has a number of conservations laws. If the perturbation violates the conservation laws, it drives the…
The Luttinger-Ward functional (LWF) has been a starting point for conserving approximations in many-body physics for 50 years. The recent discoveries of its multivaluedness and the associated divergence of the two-particle irreducible…
Even at weak to intermediate coupling, the Hubbard model poses a formidable challenge. In two dimensions in particular, standard methods such as the Random Phase Approximation are no longer valid since they predict a finite temperature…
We show exactly with an SU(N) interacting model that even if the ambiguity associated with the placement of the chemical potential, $\mu$, for a T=0 gapped system is removed by using the unique value $\mu(T\rightarrow 0)$, Luttinger's sum…
We present a theory of the dynamical two-particle response function in the Hubbard model based on the time-dependent Gutzwiller approximation. The results are in excellent agreement with exact diagonalization on small clusters and give…
We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be…
The analyticity of response functions and scattering amplitudes implies powerful relations between low-energy observables and the underlying short-distance dynamics. These 'IR/UV' relations are rooted in basic physical principles, such as…
We consider a field $f \circ T_1^{i_1} \circ \cdots \circ T_d^{i_d}$ where $T_1, \dots , T_d$ arecommuting transformations, one of them at least being ergodic. Considering the case of commuting filtrations, we are interested by giving…
The conserving approximation scheme to many-body problems was developed by Kadanoff and Baym using the functional-derivative approach. Another approach for the Hubbard model also satisfies conservation laws, but in addition it satisfies the…
Based on the self-energy-functional approach proposed recently [M. Potthoff, Eur. Phys. J. B 32, 429 (2003)], we present an extension of the cluster-perturbation theory to systems with spontaneously broken symmetry. Our method applies to…
The limit of small entropy production is reached in relaxing systems long after preparation, and in stationary driven systems in the limit of small driving power. Surprisingly, for extended systems this limit is not in general the…
In this paper, we obtain sufficient conditions in terms of projective criteria under which the partial sums of a stationary process with values in ${\mathcal{H}}$ (a real and separable Hilbert space) admits an approximation, in…
The Thomas Kuhn Reich sum rules and the sum-over-states (SOS) expression for the hyperpolarizabilities are truncated when calculating the fundamental limits of nonlinear susceptibilities. Truncation of the SOS expression can lead to an…
We present important use cases and limitations when considering results obtained from Cluster Perturbation Theory (CPT). CPT combines the solutions of small individual clusters of an infinite lattice system with the Bloch theory of…
We obtain a strong invariance principle for nonconventional sums and applying this result we derive for them a version of the law of iterated logarithm, as well as an almost sure central limit theorem. Among motivations for such results are…
There is a need to go beyond the narrow resonance approximation for QCD sum-rule channels which are likely to exhibit sensitivity to broad resonance structures. We first discuss how the first two Laplace sum rules are altered when one goes…
A sum rule which relates a stress-energy tensor correlator to thermodynamic functions is examined within the context of a simple non-conformal gravity dual. Such a sum rule was previously derived using AdS/CFT for conformal $\mathcal{N} =…
We study the renormalization group flow of the Luttinger-Ward functional and of its two-particle irreducible vertex functions, given a cut-off in the two-particle interaction. We derive a conserving approximation to the flow and relate it…