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Center for Nonlinear Studies |
Orbital is a degree of freedom independent of charge and spin, which plays important roles in magnetism and superconductivity in transition-metal-oxides. Recently, cold atom optical lattices have provided a new opportunity to investigate orbital physics. In this talk, we will present novel features of orbital physics that are not easily accessible in solid state systems. We predicted that bosons, when pumped into high orbital bands of optical lattices, exhibit a class of novel superfluid states with complex-valued condensate wave-functions spontaneously breaking time-reversal symmetry. These states are beyond the scope of the "no-node" theorem which applies to most well-known states of bosons. They exhibit unconventional symmetries in analogy to those of unconventional superconduc-tivity. Our prediction has been experimentally observed by Hemerich’s group at Ham-burg, who verified the p-wave symmetry through matter-wave interference and time-of-flight measurements. For orbital fermions, we focus on itinerant ferromagnetism (FM), i.e. FM with Fermi surfaces, which is a hard-core problem of strong correlation physics. The mean-field type Stoner criterion neglects correlation effects and thus too much over-estimates the FM tendency. In fact, even under very strong repulsions, typically electrons in solids usually remain paramagnetic. Furthermore, the Curie-Weiss metal phase above Curie temperature is also a long-standing problem exhibiting a dichotomic nature: The spin channel is local moment-like and incoherent while the charge channel remains co-herent. In spite of these difficulties, based on unambiguous non-perturbative studies, we predict the existence of the itinerant FM phase with high Curie temperatures in the p-orbital bands. We established a series of theorems proving the ground state FM phase over a large region of fermion fillings and performed sign-problem free quantum Monte-Carlo simulations. The critical and finite-size scalings of magnetic phase transitions are performed based on which Curie temperatures are extracted at high numeric precisions. Our results also apply to certain types of d-orbital transition-metal oxides in solid state systems.
Host: Shizeng Lin