Many Body Effects in Low-Dimensional Hubbard Model : 低次元ハバード模型に於ける多体効果

博巳 大塚

Kenta Shiina

Fabrizio Dolcini, Arianna Montorsi

The experimental advances in cold atomic and molecular gases stimulate the investigation of lattice correlated systems beyond the conventional on-site Hubbard approximation, by possibly including multiparticle processes. We study fermionic extended Hubbard models in a one-dimensional lattice with different types of particle couplings, including also three- and four-body interactions up to nearest neighboring sites. By using the bosonization technique, we investigate the low-energy regime and determine the conditions for the appearance of ordered phases, for arbitrary particle filling. We find that three- and four-body couplings may significantly modify the phase diagram. In particular, diagonal three-body terms that directly couple the local particle densities have qualitatively different effects from off-diagonal three-body couplings originating from correlated hopping, and favor the appearance of a Luther-Emery phase even when two-body terms are repulsive. Furthermore, the four-body coupling gives rise to a rich phase diagram and may lead to the realization of the Haldane insulator phase at half-filling.

修 成清

Jianzhong Zheng

This thesis addresses the question of a strongly interacting many-body problem: the Hubbard model on one- and two-dimensional lattices. The technique employed is the small-cluster method wherein the full many-body Hamiltonian for finite clusters with periodic boundary conditions (PBC's) is solved exactly. We first apply this technique to an extended one-dimensional chain and a two-dimensional square-lattice Hubbard model. We then construct a two-dimensional overlayer/substrate Hubbard model with first- and second-nearest-neighbor hopping, on-site and nearest-neighbor interactions, and overlayer-site orbital energy. The ground-state properties are investigated and discussed in a many-body picture.

Ian P. Mc Culloch, M. Gulácsi

The physical properties of two-dimensional interacting electron systems are of great current interest. An open question in the physics of low-dimensional fermionic models is whether their properties are described by standard Fermi-liquid theory or whether instead they show unconventional behaviour in strongly correlated electron systems. As the two-dimensional Hubbard model is the typical example of a strongly correlated electron system, we solve for this model the two-body problem in the vicinity of a half-filled Fermi sea. The results obtained show that for a low hole concentration the well known Fermi-liquid picture fails.