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Accueil > Séminaires > Archive des séminaires d’Utinam > 2017

Pierre Nataf

Numerical methods to investigate Heisenberg SU (N ) lattice models.

mercredi 15 février 2017, 15h

salle de conférences de l’observatoire

Pierre Nataf
Institut de Physique Théorique, Ecole Polytechnique Fédérale de Lausanne, Suisse

Résumé :

Systems of multicolor fermions have recently raised considerable interest due to the possibility to experimentally study those systems on optical lattices with ultracold atoms [1].
To describe the Mott insulating phase of N -colors fermions, one can start with the SU (N ) Heisenberg Hamiltonian. In the case of one particule per site, the SU (N ) Heisenberg Hamiltonian takes the form of a Quantum permutation Hamiltonian
H = J Σi,j P <ij> , where the transposition operator P <ij> exchanges two colors on neighboring sites.
We have developped a method [2] to implement the SU (N ) symmetry in an Exact Diagonalization algorithm. In particular, the method enables one to diagonalize the Hamiltonian directly in the irreducibe representations of SU (N ), thanks to the use of standard Young tableaux [3], which are shown to form a very convenient basis to diagonalize the problem. It allowed us to prove that the ground state of the Heisenberg SU (5) model on the square lattice is long range color ordered [2] and it provided evidence that the phase of the Heisenberg SU (6) model on the Honeycomb lattice is a plaquette phase [4]. We have also extended the method to the case where there are m ≥ 1 particles per site in the fully antisymmetric [5] and symmetric [6] irreps of SU (N ) in order to study SU (N ) critical chains.
In this seminar, I will not only present our results but also devote some time to describe other numerical methods (such as DMRG [7] , Quantum Monte Carlo [8], Variational Monte Carlo[5], etc...) which are useful in the simulation of those systems and which illustrate the kind of numerical tools that theoretical physicists are currently developping in the field of strongly correlated systems.