Multiparticle Interactions of Zero-Range Potentials

V. E. Zobov, A. A. Lundin

J. H. Macek, S. Yu. Ovchinnikov

Victor Chulaevsky

We adapt the method of direct scaling analysis developed earlier for single-particle Anderson models, to the fermionic multiparticle models with finite or infinite interaction on graphs. Combined with a recent eigenvalue concentration bound for multiparticle systems, the new method leads to a simpler proof of the multiparticle dynamical localization with optimal decay bounds in a natural distance in the multiparticle configuration space, for a large class of strongly mixing random external potentials. Earlier results required the random potential to be IID.

W. H. Klink, W. Schweiger

W. H. Klink, S. Wickramasekara

Klaus Voelker, Sudip Chakravarty

We consider a two-dimensional electron or hole system at zero temperature and low carrier densities, where the long-range Coulomb interactions dominate over the kinetic energy. In this limit the clean system will form a Wigner crystal. Nontrivial quantum-mechanical corrections to the classical ground state lead to multiparticle exchange processes that can be expressed as an effective spin Hamiltonian involving competing interactions. Disorder will destroy the Wigner crystal on large length scales, and the resulting state is called a Wigner glass. The notion of multiparticle-exchange processes is still applicable in the Wigner glass, but the exchange frequencies now follow a random distribution. We compute the exchange frequencies for a large number of relevant exchange processes in the Wigner crystal, and the frequency distributions for some important processes in the Wigner glass. The resulting effective low-energy spin Hamiltonian should be the starting point of an analysis of the possible ground-state phases and quantum phase transitions between them. We find that disorder plays a crucial role and speculate on a possible zero-temperature phase diagram.