Exact ground states of disordered systems

Zsolt Gulácsi

Ido Kanter

We present some exact results for the ground-state wave function and the energy of disordered quantum-mechanical spin systems in any dimensions. The system contains all nearest- and some of the next-nearest-neighbor interactions. The solution is also available for some range of anisotropy. In all the cases the ground-state wave function is insensitive to the disorder.

Peter J. Forrester

Zsolt Gulácsi

We report exact multielectronic ground states dependent on electron concentration for quantum-mechanical two-dimensional disordered two-band-type many-body models in the presence of disordered hoppings and disordered repulsive finite Hubbard interactions, in fixed lattice topology considered provided by Bravais lattices. The obtained ground states lose their eigenfunction character for independent electron approximation, are perturbatively not connected to the noninteracting but disordered case, and describe a localization-delocalization transition driven by the electron concentration, being highly degenerated and paramagnetic.

Xiaodong Bai, Jiyong Fu, Tiantian Li +2 more

H. T. Diep, Héctor Giacomini

After a short introduction on frustrated spin systems, we study in this chapter several two-dimensional frustrated Ising spin systems which can be exactly solved by using vertex models. We show that these systems contain most of the spectacular effects due to the frustration: high ground-state degeneracy, existence of several phases in the ground-state phase diagram, multiple phase transitions with increasing temperature, reentrance, disorder lines, partial disorder at equilibrium. Evidences of such effects in non solvable models are also shown and discussed.