28 citations · 124 across the 28 of their papers we have counts for
10 papers · 1 filter
A discrete Smorodinsky--Winternitz II superintegrable system
Pierre-Antoine Bernard, Vutha Vichhea Chea, Luc Vinet
We construct a discrete Smorodinsky--Winternitz II superintegrable system on a triangular region of the two-dimensional square lattice. The model is built from a pair of commuting…
Exactly solvable inhomogeneous XY spin chain
Pierre-Antoine Bernard, Nicolas Crampé, Quentin Labriet +2
Analytical expressions for the eigenvalues of certain inhomogeneous XY spin chains are computed. These models are rewritten in terms of free-fermion models using a well-known Jorda…
A -version of the relation between the hypercube, the Krawtchouk chain and Dicke states
Pierre-Antoine Bernard, Étienne Poliquin, Luc Vinet
It is shown how the spin chain based on the dual -Krawtchouk polynomials is connected to a weighted hypercube through the use of -Dicke states. The representation theoretic u…
Computation of entanglement entropy in inhomogeneous free fermions chains by algebraic Bethe ansatz
Pierre-Antoine Bernard, Gauvain Carcone, Nicolas Crampe +1
The computation of the entanglement entropy for inhomogeneous free fermions chains based on q-Racah polynomials is considered. The eigenvalues of the truncated correlation matrix a…
Bethe ansatz diagonalization of the Heun-Racah operator
Pierre-Antoine Bernard, Gauvain Carcone, Nicolas Crampe +1
The Heun-Racah operator is diagonalized with the help of the modified algebraic Bethe ansatz. This operator is the most general bilinear expression in two generators of the Racah a…
Time and band limiting operator and Bethe ansatz
P. -A. Bernard, N. Crampe, L. Vinet
The time and band limiting operator is introduced to optimize the reconstruction of a signal from only a partial part of its spectrum. In the discrete case, this operator commutes…
Entanglement of Free Fermions on Johnson Graphs
Pierre-Antoine Bernard, Nicolas Crampe, Luc Vinet
Free fermions on Johnson graphs are considered and the entanglement entropy of sets of neighborhoods is computed. For a subsystem composed of a single neighborhood, an ana…
Heun operator of Lie type and the modified algebraic Bethe ansatz
Pierre-Antoine Bernard, Nicolas Crampe, Dounia Shaaban Kabakibo +1
The generic Heun operator of Lie type is identified as a certain -Gaudin magnet Hamiltonian in a magnetic field. By using the modified algebraic Bethe ansatz introduced to diag…
Superintegrability and the dual Hahn algebra in superconformal quantum mechanics
Pierre-Antoine Bernard, Julien Gaboriaud, Luc Vinet
A two-dimensional superintegrable system of singular oscillators with internal degrees of freedom is identified and exactly solved. Its symmetry algebra is seen to be the dual …
A graph with fractional revival
Pierre-Antoine Bernard, Ada Chan, Érika Loranger +2
An example of a graph that admits balanced fractional revival between antipodes is presented. It is obtained by establishing the correspondence between the quantum walk on a hyperc…