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In this work we present a coupled-cluster theory for the propagation of multireference electronic systems initiating at general quantum mechanical states. Our formalism is based on the infinitesimal analysis of modified cluster operators,…
The one-dimensional contact process is analyzed by a cluster approximation. In this approach, the hierarchy of rate equations for the densities of finite length empty intervals are truncated under the assumption that adjacent intervals are…
The DCA$^+$ algortihm was recently introduced to extend the dynamic cluster approximation (DCA) with a continuous lattice self-energy in order to achieve better convergence with cluster size. Here we extend the DCA$^+$ algorithm to the…
Methods which aim at universal applicability must be able to describe both weak and strong electronic correlation with equal facility. Such methods are in short supply. The combination of symmetry projection for strong correlation and…
The one-dimensional Hubbard model is investigated by means of two different cluster schemes suited to introduce short-range spatial correlations beyond the single-site Dynamical Mean-Field Theory, namely the Cluster-Dynamical Mean-Field…
A one-dimensional model of electrons locally coupled to spin-1/2 degrees of freedom is studied by numerical techniques. The model is one in the class of $dynamic$ $Hubbard$ $models$ that describe the relaxation of an atomic orbital upon…
A general expansion scheme based on the concept of linked cluster expansion from the theory of classical spin systems is constructed for models of interacting electrons. It is shown that with a suitable variational formulation of mean-field…
In this tutorial-style review we discuss basic concepts of coupled cluster theory and recent developments that increase its computational efficiency for calculations of molecules, solids and materials in general. We will touch upon the…
Previously we have indicated the relationship between quantum groups and strings via WZWN models. In this note we discuss this relationship further and point out its possible applications to cuprates and related materials. The connection…
We study cluster perturbation theory [Phys. Rev. Lett. \textbf{84}, 522 (2000)] when auxiliary field quantum Monte Carlo method is used for solving the cluster hamiltonian. As a case study, we calculate the spectral functions of the Hubbard…
We outline how the coupled cluster method of microscopic quantum many-body theory can be utilized in practice to give highly accurate results for the ground-state properties of a wide variety of highly frustrated and strongly correlated…
A new approximate scheme, DSUB$m$, is described for the coupled cluster method. We then apply it to two well-studied (spin-1/2 Heisenberg antiferromagnet) spin-lattice models, namely: the $XXZ$ and the $XY$ models on the square lattice in…
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…
A possibility of the electronic origin of the high-temperature superconductivity in cuprates is probed with the quantum Monte Carlo method by revisiting the three-band Hubbard model comprising Cu$3d_{x^2-y^2}$ and O$2p_\sigma$ orbitals. The…
We study the fluctuations responsible for pairing in the $d$-wave superconducting state of the two-dimensional Hubbard model at intermediate coupling within a cluster dynamical mean-field theory with a numerically exact quantum impurity…
Significant progress towards a theory of high-temperature superconductivity in cuprates has been achieved via the study of effective one- and three-band Hubbard models. Nevertheless, material-specific predictions, while essential for…
This study introduces a systematic approach for analyzing strongly correlated systems by adapting the conventional quantum cluster method to a quantum circuit model. We have developed a more concise formula for calculating the cluster's…
We study the Cu_{5}O_{4} cluster by exact diagonalization of a three-band Hubbard model and show that bound electron or hole pairs are obtained at appropriate fillings, and produce superconducting flux quantisation. The results extend…
We review how the (quantum) cluster algebra naturally emerges in the study of four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories.
We present the algorithmic details of the dynamical cluster approximation (DCA) algorithm. The DCA is a fully-causal approach which systematically restores non-local correlations to the dynamical mean field approximation (DMFA). The DCA is…