Rectification induced by geometry in two-dimensional quantum spin lattices

Quantum geometry of 3-dimensional lattices

We study geometric consistency relations between angles on 3-dimensional (3D) circular quadrilateral lattices — lattices whose faces are planar quadrilaterals inscribable into a circle. We show that these relations generate canonical transformations of a remarkable “ultra-local” Poisson bracket algebra defined on discrete 2D surfaces consisting of circular quadrilaterals. Quantization of this s...

Simulations of Quantum XXZ Models on Two-Dimensional Frustrated Lattices

We report recent progress in the study of a particular class of spin 1/2 XXZ model on two-dimensional lattices with frustrated diagonal and unfrustrated off-diagonal interactions. Quantum Monte Carlo simulations can be constructed without a sign problem, however they require non-trivial algorithmic advances in order to combat freezing tendencies. We discuss results obtained using these techniqu...

Dipole solitons in optically induced two-dimensional photonic lattices.

Dipole solitons in a two-dimensional optically induced photonic lattice are theoretically predicted and experimentally demonstrated for the first time to our knowledge. It is shown that such dipole solitons are stable and robust under appropriate conditions. Our experimental results are in good agreement with theoretical predictions.

Quantum nanostructures in strongly spin-orbit coupled two- dimensional systems

Quantum Phases in Two-dimensional Frustrated Spin-1/2 Antiferromagnets

Investigating various spin-1/2 systems in two dimensions (2d), by means of exact diagonalization (ED) on small samples of N spins, we have found, up to now, four kinds of antiferromagnetic phases at T=0. Two of them display long range order (LRO): Néel or Valence Bond Crystal (VBC) LRO. The others are two different Spin-Liquids. The Néel case may be qualified as semi-classical: it is a groundst...