8 papers
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…
Analytical Angle-Finding and Series Expansions for Quantum Signal Processing via Orthogonal Polynomial Theory
Pierre-Antoine Bernard, Nathan Wiebe
Quantum signal processing is a powerful framework in quantum algorithms, playing a central role in Hamiltonian simulation and related applications. The sequence of polynomials impl…
Entanglement Hamiltonian and orthogonal polynomials
Pierre-Antoine Bernard, Riccarda Bonsignori, Viktor Eisler +2
We study the entanglement Hamiltonian for free-fermion chains with a particular form of inhomogeneity. The hopping amplitudes and chemical potentials are chosen such that the singl…
Entanglement of Inhomogeneous Free Bosons and Orthogonal Polynomials
Pierre-Antoine Bernard, Rafael I. Nepomechie, Gilles Parez +3
In this paper, we investigate the ground-state entanglement entropy in inhomogeneous free-boson models in one spatial dimension. We develop a powerful method to extract the leading…
Distinctive features of inhomogeneous spin chains
Pierre-Antoine Bernard, Gilles Parez, Luc Vinet
This review presents recent developments in the study of inhomogeneous XX spin chains, highlighting results on perfect state transfer, out-of-equilibrium stationary dynamics in ope…
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…