The use of exactly solvable Richardson-Gaudin models to describe the physics of systems
with strong pair correlations is reviewed. The article begins with a brief discussion of …

In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of
the energy spectra and form factors (operator matrix elements in the basis of Hamiltonian …

We consider the flavor evolution of a dense neutrino gas by taking into account both vacuum
oscillations and self-interactions of neutrinos. We examine the system from a many-body …

We determine the zero-temperature quantum phase diagram of apx+ ipy pairing model
based on the exactly solvable hyperbolic Richardson-Gaudin model. We present analytical …

We present a numerical approach which allows the solving of Bethe equations whose
solutions define the eigenstates of Gaudin models. By focusing on a different set of …

A new approach for solving the Bethe ansatz (Gaudin-Richardson) equations of the
standard pairing problem is established based on the Heine-Stieltjes correspondence. For k …

We obtain analytically close forms of benchmark quantum dynamics of the collapse and
revival (CR), the reduced density matrix, Von Neumann entropy, and fidelity for the XXZ …

Background: The reduced, level-independent, Bardeen-Cooper-Schrieffer Hamiltonian is
exactly diagonalizable by means of a Bethe ansatz wave function, provided the free …

Using the well-known trigonometric six-vertex solution of the Yang–Baxter equation we
derive an integrable pairing Hamiltonian with anyonic degrees of freedom. The exact …

Abstract The extended Heine–Stieltjes polynomials associated with a special Lipkin–
Meshkov–Glick (LMG) model corresponding to the standard two-site Bose–Hubbard model …