为了描述基态拓扑量子相变.ppt

* M. Sarachik, et al., Phys. Rev. 135, A1041 (1964). Subtracted residual and lattice (phonon) contributions Perturbation theory of a magnetic impurity problem Resistance Minimum in Dilute Magnetic Alloys Jun Kondo, Progress of Theoretical Physics, 32, 37-- 49 (1964). Electrical resistance and spin magnetic susceptibility Born approximation -- classical results Kondo model: Quantum corrections Electron scattering Electron-hole pair involved scattering Second order spin-flip scatterings Perturbation theory is divergent as T→0K, i.e., the Kondo problem. Emergence of the Kondo resonance as T → 0K from RG study of the Anderson impurity model B. Horvatic, D. Sokcevic, and V. Zlatic, Phys. Rev. B 36, 675 (1987). Emergence of a singlet bound state between the impurity and the conduction electrons as the energy scale goes down to the low energy limit. The phase shift of other conduction electrons off the bound state is the maximal one – the unitary limit. A universal crossover from weak to strong couplings i.e., from lnT to T2 behavior --- the Kondo physics Spin fluctuations: Kondo effect Kondo spin screening effect Tk ↓ F. T. Hedgecock and C. Rizzuto, Phys. Rev. 163, 517 (1967). From the Kondo problem to rare earth/actinide compounds Y. Onuki and T. Komastubara, J. Magnetism Magnetic Materials, 54, 433 (1986). Heavy Fermion Metals Superconductors History heavy fermions: First HF metal, CeAl3, was measured in 1975. Effective charge-carrier masses are hundreds of times the bare electron mass, and the relevant energy scales are very small. First HF superconductor, CeCu2Si2 was observed in 1979; Other HF superconductors were also found: UBe13, UPt3, URu2Si2. Typical Kondo lattice systems: CeCu2Si2 and CeAl3 Z. Fisk, et.al., Nature 320, 124 (1986). 对二维量子自旋1/2并可用于拓扑量子计算的多体系统 - Kitaev模型，借助于Jordan-Wigner变换将该模型严格约化为一个在静态Z_2规范场下的自由Majorana费米系统。这是迄今极少有的量子二维可严格求解的多体系统。 拓扑量子相变及其微观刻画的严格理论 X.Y.Feng, G.M.Zhang and T.Xiang, Physical Review Letters 98，087204（2007）