2013 Fiscal Year Final Research Report
Algebraic approaches to strongly correlated electron systems
| Project/Area Number |
23740298
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Mathematical physics/Fundamental condensed matter physics
|
|---|
| Research Institution | Gakushuin University |
|---|
Principal Investigator |
KATSURA HOSHO 学習院大学, 理学部, 准教授 (80534594)
|
|---|
| Project Period (FY) |
2011 – 2013
|
| Keywords | 強相関電子系 / 物性基礎論 / 数理物理 / エンタングルメント / 記号計算 |
|---|
| Research Abstract |
We have studied a variety of lattice models that describe systems of strongly interacting fermions, bosons, and spins. Examples of the models include Bose- and Fermi-Hubbard models, and the quantum hard-square model. Various exact and/or rigorous results were obtained by exploiting the integrability or using some mathematical tools like the Perron-Frobenius theorem. For example, we have proved a natural analogue of Nagaoka's theorem in the SU(n) Hubbard model. We have also studied entanglement spectra of solvable lattice models in two dimensions by combining analytical and numerical techniques. The results obtained suggest that the entanglement Hamiltonian of the valence-bond-solid (VBS) state is well described by the one-dimensional Heisenberg model.
|
