Contributor info: Prof. Stijn De Baerdemacker

Klaas Gunst, Dimitri Van Neck, Peter Andreas Limacher, Stijn De Baerdemacker

SciPost Chem. 1, 001 (2021) · published 15 January 2021 | Toggle abstract · pdf

We employ tensor network methods for the study of the seniority quantum number -- defined as the number of unpaired electrons in a many-body wave function -- in molecular systems. Seniority-zero methods recently emerged as promising candidates to treat strong static correlations in molecular systems, but are prone to deficiencies related to dynamical correlation and dispersion. We systematically resolve these deficiencies by increasing the allowed seniority number using tensor network methods. In particular, we investigate the number of unpaired electrons needed to correctly describe the binding of the neon and nitrogen dimer and the $D_{6h}$ symmetry of benzene.

Pieter W. Claeys, Dimitri Van Neck, Stijn De Baerdemacker

SciPost Phys. 3, 028 (2017) · published 24 October 2017 | Toggle abstract · pdf

We present the inner products of eigenstates in integrable Richardson-Gaudin models from two different perspectives and derive two classes of Gaudin-like determinant expressions for such inner products. The requirement that one of the states is on-shell arises naturally by demanding that a state has a dual representation. By implicitly combining these different representations, inner products can be recast as domain wall boundary partition functions. The structure of all involved matrices in terms of Cauchy matrices is made explicit and used to show how one of the classes returns the Slavnov determinant formula. This framework provides a further connection between two different approaches for integrable models, one in which everything is expressed in terms of rapidities satisfying Bethe equations, and one in which everything is expressed in terms of the eigenvalues of conserved charges, satisfying quadratic equations.