Related papers: Cluster diagonalization in systematically expanded…
We propose a hierarchical correlation clustering method that extends the well-known correlation clustering to produce hierarchical clusters applicable to both positive and negative pairwise dissimilarities. Then, in the following, we study…
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…
The coherent potential approximation, CPA, is a useful tool to treat systems with disorder. Cluster theories have been proposed to go beyond the translation invariant single-site CPA approximation and include some short range correlations.…
By parameterizing the t-j model we present a new electron correlation model with one free parameter for high-temperature superconductivity. This model is of $SU_{q}(1,2)$ symmetry. The energy spectrums are shown to be modulated by the free…
We propose a novel probabilistic approach to multilevel clustering problems based on composite transportation distance, which is a variant of transportation distance where the underlying metric is Kullback-Leibler divergence. Our method…
In the strong electron-electron (e-e) interaction limit each atomic site is constrained to be either empty or singly occupied. One can treat this scenario by fractionalizing the electrons into spin and charge degrees of freedom. We use the…
Efficient and accurate computational methods for dealing with interacting electron problems on a lattice are of broad interest to the condensed matter community. For interacting Hubbard models, we introduce a cluster slave-particle approach…
Dynamical linked cluster expansions are linked cluster expansions with hopping parameter terms endowed with their own dynamics. They amount to a generalization of series expansions from 2-point to point-link-point interactions. We outline…
We present an efficient exact diagonalization scheme for the extended dynamical mean-field theory and apply it to the extended Hubbard model on the square lattice with nonlocal charge-charge interactions. Our solver reproduces the phase…
The generalized t-J model conserving the number of double occupancies is constructed from the Hubbard model at and in the vicinity of half-filling at strong coupling. The construction is realized by a self-similar continuous unitary…
We derive and implement a new way of solving coupled cluster equations with lower computational scaling. Our method is based on decomposition of both amplitudes and two electron integrals, using a combination of tensor hypercontraction and…
In this paper, I outline several conceptual and methodological issues related to modeling individual and group processes embedded in clustered/hierarchical data structures. We position multilevel modeling techniques within a broader set of…
We perform time-resolved exact diagonalization of the Hubbard model with time dependent hoppings on small clusters of up to $12$ sites. Here, the time dependence originates from a classic electromagnetic pulse, which mimics the impact of a…
Subspace clustering algorithms are notorious for their scalability issues because building and processing large affinity matrices are demanding. In this paper, we introduce a method that simultaneously learns an embedding space along…
We discuss some applications of higher symmetry groups to condensed matter systems. We give special attention to the groups SO(n) (n = 4, 5, 6, 8) in the two-dimensional Hubbard model and its generalizations, which model the high T_c…
A novel reduced-scaling, general-order coupled-cluster approach is formulated by exploiting hierarchical representations of many-body tensors, combined with the recently suggested formalism of scale-adaptive tensor algebra. Inspired by the…
In quantum chemistry, one of the most important challenges is the static correlation problem when solving the electronic Schr\"odinger equation for molecules in the Born--Oppenheimer approximation. In this article, we analyze the tailored…
In this article, we propose the use of partitioning and clustering methods as an alternative to Gaussian quadrature for stochastic collocation. The key idea is to use cluster centers as the nodes for collocation. In this way, we can extend…
Cluster variables have recently revolutionized numerical work in certain models involving fermionic variables. This novel representation of fermionic partition functions is continuing to find new applications. After describing results from…
Along the ideas of Curtain and Glover, we extend the balanced truncation method for infinite-dimensional linear systems to bilinear and stochastic systems. Specifically , we apply Hilbert space techniques used in many-body quantum mechanics…