可积系统与低维凝聚态模型

Much progress has been achieved by using nonperturbation approach to strongly correlated electron systems according to the original proposal for the National Natural Science Foundation project. Additionally, our research also swiftly involved the new highlight of correlated Boson system which has been absorbed more and more attention. The Hubbard model for electrons with orbital degeneracy is shown to have an underlying SUd(4) symmetry of spin-orbital double. A hidden charge SUc(4) symmetry is exposed and an extended Lieb-Mattis transformation which maps these two symmetries into each other is given. On the basis of elementary degenerate perturbative theory, it is shown that the system with strong repulsive coupling is equivalent to a SO(6) Heisenberg magnet at half-filling and a SU(4) one at quarter-filling.The features of ground state and low-lying excitations in one dimension are indicated according to exact solutions. Various possibilities of symmetry breaking are also given. The Lieb-Schultz-Mattis theorem is extended to generalized Heisenberg models related to non-exceptional Lie algebras.It is shown that there are no energy gaps above the ground sates for SO(4), Sp(2) and SU(4) Heisenberg models, gaps are suspected to occur in SO(5) and SO(6) models. The nondegenerate ground state for these models is rigorously proven. We study a one-dimensional Bose system with repulsive delta-function interaction in the presence of an SU(2) intrinsic degree of freedom on the basis of the coordinate Bethe-ansatz. The ground state and the low-lying excitations are determined by both numerical and analytical methods. It is shown that the ground state is an isospin-ferromagnetic state, and the excitations are composed of three elementary particles: holons, antiholons, and isospinons. Besides, quantum transport through a resonant cavity with multileads was studied and the oscillation properties of mesoscopic RLC circuits was discussed.

用量子可积系统及低维场论的有关方法研究凝聚态物理中的自旋系统和强关联电子系场Ｖ饕泄斓兰虿⒋判圆牧厦?鲁汀格.液体与Kondo杂质系.统,.电子间相互作用摸型等；低维摸型中非平.庸物理边界条件的效应。侧重用非微扰方法研究基态、低激发态.、关联函数及热力学性质等.。研究结果有助于揭示高温超导机理.和理解反铁磁。