Related papers: Coupled cluster theory: Towards an algebraic geome…
Coupled cluster theory is one of the most popular post-Hartree-Fock methods for ab initio molecular quantum chemistry. The finite-size error of the correlation energy in periodic coupled cluster calculations for three-dimensional insulating…
Rational approximations of functions with singularities can converge at a root-exponential rate if the poles are exponentially clustered. We begin by reviewing this effect in minimax, least-squares, and AAA approximations on intervals and…
The central problem in electronic structure theory is the computation of the eigenvalues of the electronic Hamiltonian -- an unbounded, self-adjoint operator acting on a Hilbert space of antisymmetric functions. Coupled cluster (CC)…
Atomic nuclei can exhibit shape coexistence and multi-reference physics that enters in their ground states, and to accurately capture the ensuing correlations and entanglement is challenging. We address this problem by applying…
We introduce perturbation and coupled-cluster theories based on a cluster mean-field reference for describing the ground state of strongly-correlated spin systems. In cluster mean-field, the ground state wavefunction is written as a simple…
We present a combinatorial model for cluster algebras of type $D_n$ in terms of centrally symmetric pseudotriangulations of a regular $2n$-gon with a small disk in the centre. This model provides convenient and uniform interpretations for…
A unitary coupled-cluster (UCC) form for the wavefunction in the variational quantum eigensolver has been suggested as a systematic way to go beyond the mean-field approximation and include electron correlation in solving quantum chemistry…
The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…
Motivated by the cluster structure of two-loop scattering amplitudes in N=4 Yang-Mills theory we define "cluster polylogarithm functions". We find that all such functions of weight 4 are made up of a single simple building block associated…
Arithmetic combinatorics is often concerned with the problem of bounding the behaviour of arbitrary finite sets in a group or ring with respect to arithmetic operations such as addition or multiplication. Similarly, combinatorial geometry…
We give a uniform geometric realization for the cluster algebra of an arbitrary finite type with principal coefficients at an arbitrary acyclic seed. This algebra is realized as the coordinate ring of a certain reduced double Bruhat cell in…
In single-reference coupled-cluster (CC) methods, one has to solve a set of non-linear polynomial equations in order to determine the so-called amplitudes which are then used to compute the energy and other properties. Although it is of…
There is a growing interest in characterizing circular data found in biological systems. Such data are wide ranging and varied, from signal phase in neural recordings to nucleotide sequences in round genomes. Traditional clustering…
Quantum periodic cluster methods for strongly correlated electron systems are reformulated and developed. The reformulation and development are based on a canonical transformation which periodizes the fermions in the cluster space. The…
This article presents an in-depth educational overview of the latest mathematical developments in coupled cluster (CC) theory, beginning with Schneider's seminal work from 2009 that introduced the first local analysis of CC theory. We offer…
Electronic structure methods built around double-electron excitations have a rich history in quantum chemistry. However, it seems to be the case that such methods are only suitable in particular situations and are not naturally equipped to…
Unitary Coupled Cluster (UCC) theory is a promising variational method for electronic structure calculations, especially for strongly correlated systems and quantum computers. However, its practical application is limited by the steep…
In this paper, we have developed a unitary variant of a double exponential coupled cluster theory, which is capable of mimicking the effects of connected excitations of arbitrarily high rank, using only rank-one and rank-two parametrization…
Quantum cluster approaches offer new perspectives to study the complexities of macroscopic correlated fermion systems. These approaches can be understood as generalized mean-field theories. Quantum cluster approaches are non-perturbative…
We discuss an initial implementation of the coupled-cluster method for nuclear structure calculations and apply our method to He-4. We will discuss the future directions that this research will take as we move from method testing and…