Related papers: Density Matrices of Seniority-Zero Geminal Wavefun…
We develop a bivariational principle for an antisymmetric product of nonorthogonal geminals. Special cases reduce to the antisymmetric product of strongly-orthogonal geminals (APSG), the generalized valence bond-perfect pairing (GVB-PP),…
Geminal wavefunctions have been employed to model strongly-correlated electrons. These wavefunctions represent products of weakly-correlated pairs of electrons and reasonable approximations are computable with polynomial cost. In…
Seniority-zero geminal wavefunctions are known to capture bond-breaking correlation. Among this class of wavefunctions, Richardson-Gaudin states stand out as they are eigenvectors of a model Hamiltonian. This provides a clear physical…
Strong pairing correlations are responsible for superconductivity and off-diagonal long range order in the two-particle density matrix. The antisymmetrized geminal power wave function was championed many years ago as the simplest model that…
Wavefunction forms based on products of electron pairs are usually constructed as closed-shell singlets, which is insufficient when the molecular state has a nonzero spin or when the chemistry is determined by $d$- or $f-$electrons. A set…
Eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian, Richardson-Gaudin (RG) states, are used as a variational wavefunction Ansatz for strongly-correlated electronic systems. These states are geminal products whose coefficients…
Richardson-Gaudin (RG) states are employed as a variational wavefunction ansatz for strongly correlated isomers of H$_4$ and H$_{10}$. In each case a single RG state describes the seniority-zero sector quite well. Simple natural orbital…
Recently, ground state eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian, Richardson-Gaudin (RG) states, have been employed as a wavefunction ansatz for strong correlation. This wavefunction physically represents a…
This chapter gives an overview of Richardson-Gaudin states which represent weakly correlated pairs of electrons. They are parametrized by sets of numbers obtained from non-linear equations. The best method to solve these equations is…
Slater determinants underpin most electronic structure methods, but orbital-based approaches often struggle to describe strong correlation efficiently. Geminal-based theories, by contrast, naturally capture static correlation in…
The ground, one- and two-particle states of the (1+1)-dimensional massive sine-Gordon field theory are investigated within the framework of the Gaussian wave-functional approach. We demonstrate that for a certain region of the…
We present an overview of the mathematical structure of geminal theory within the seniority formalism and bi-variational principle. Named after the constellation, geminal wavefunctions provide the mean-field like representation of…
We derive a powerful yet simple method for analyzing the local density of states in gapless one dimensional fermionic systems, including extensions such as momentum dependent interaction parameters and hard-wall boundaries. We study the…
Seniority-zero wavefunctions describe bond-breaking processes qualitatively. As eigenvectors of a model Hamiltonian, Richardson-Gaudin states provide a clear physical picture and allow for systematic improvement via standard single…
The scattering of Dirac fermions on the sine-Gordon kink is studied both analytically and numerically. To achieve invariance with respect to a discrete symmetry, the sine-Gordon model is treated as a nonlinear $\sigma$-model with a circular…
In previous research, we tested the wave function format of a linear combination of several antisymmetrized geminal power states. A numerical problem in the geminal matrices was noted, which made the total energies of electronic systems…
The density of vibrational states $g(\omega)$ of an amorphous system is studied by using the random-matrix theory. Taking into account the most important correlations between elements of the random matrix of the system, equations for the…
A fermion node is subset of fermionic configurations for which a real wave function vanishes due to the antisymmetry and the node divides the configurations space into compact nodal cells (domains). We analyze the properties of fermion…
We investigated some variational methods to compute a wavefunction based on antisymmetric product of geminals (APG). The Waring decomposition on the APG wavefunction leads a finite sum of antisymmetrized geminal power (AGP) wavefunctions,…
Interest in modulated paired states, long sought since the first proposals by Fulde and Ferrell and by Larkin and Ovchinnikov, has grown recently in the context of strongly coupled superconductors under the name of pair density wave.…