Dynamic generation of spinorbit coupling自旋轨道耦合的动态生成.ppt

Collaborators Outline Outline Strong coupling analysis at half-filling Pseudospin SU(2) algebra Outline The sign problem in spin 1/2 Hubbard model Summary The T (time-reversal) invariant decomposition. Applicable in a wide class of multi-band and high models at any doping level and lattice geometry. Need a general criterion independent of factorizibility of fermion determinants. A general criterion: symmetry principle Reference: C. Wu and S. C. Zhang, Phys. Rev. B 71, 155115(2005); C. Capponi, C. Wu, and S. C. Zhang, Phys. Rev. B 70, 220505(R) (2004). C. Wu and S. C. Zhang, Phys. Rev. Lett. 91, 186402 (2003). Eigenvalues of I+B appear in complex conjugate pairs (l, l*). If l is real, then it is doubly degenerate. T-invariant decomposition CW and S. C. Zhang, PRB 71, 155115 (2005); E. Koonin et. al., Phys. Rep. 278 1, (1997) Theorem: If there exists an anti-unitary transformation T for any H-S field configuration, then T may not be the physical time reversal operator. Generalized Kramer’s degeneracy I+B may not be Hermitian, and even not be diagonalizable. U0: H-S decoupling in the density channel. T-invariant decomposition ? absence of the sign problem U0: H-S decoupling in the spin channel. Generally speaking, the sign problem appears. The factorizibility of fermion determinants is not required. Validity at any doping level and lattice geometry. Application in multi-band, high spin models. Distribution of eigenvalues . T=Time-reversal*flip two layers Absence of the sign problem at g, g’, gc0, . T-invariant operators: total density, total density; bond AF, bond current. The 2D staggered ground state current phase in a bi-layer model. Spin-orbit coupling induced ferromagnetism in the DDW phase in La2-xBaxCu2O4. T-invariant decomposition and the sign problem in quantum Monte Carlo simulations. Now, we can look at the sign problem in the Hubbard model from this perspective. In the U0 ca