Novel Orbital Physics – Unconventional Bose-Einstein Condensation, Ferromagnetism, and Curie-Weiss Metal in Optical Lattices

Synopsis

Orbital is a degree of freedom independent of charge and spin. It plays an important role in physical properties of transition-metal-oxides including superconductivity and magnetism. The recent developments of optical lattices have opened up an opportunity to study novel features of orbital physics that are not easily accessible in solid state systems.

We predicted that cold bosons, when pumped into high orbital bands of optical lattices, exhibit a class of novel superfluid states spontaneously breaking time-reversal symmetry. In analogy to unconventional superconductivity, their condensate wavefunctions are complex-valued possessing unconventional symmetries, which are beyond the scope of “no-node” theorem for most well-known states of bosons. A p-wave condensate of orbital bosons has been experimentally realized by Hemerich’s group at Hamburg University, and its unconventional symmetry has been verified through the matter-wave interference measurements. For orbital fermions, we performed non-perturbative studies on itinerant ferromagnetism (FM), a hard core problem of strong correlation physics. Itinerant FM is based on Fermi surface instability rather than ordering of local spin moments. The well-known Stoner criterion overestimates the FM tendency by neglecting correlation effects. Even under very strong repulsions, electrons in solids usually remain paramagnetic. Furthermore, the paramagnetic metal phase above the Curie temperature, i.e., the Curie-Weiss metal state, is a long-standing challenge. It exhibits a dichotomic nature: The spin channel is incoherent, i.e., local moment-like, while the charge channel remains coherent. In spite of these difficulties, we proposed the existence of itinerant FM phases with high Curie temperatures in the p-orbital bands. A series of theorems are proved setting up the ground state FM phases over a large region of fermion fillings. The Curie-Weiss metal phase and the critical scalings of the FM transitions are studied via the sign-problem free quantum Monte-Carlo simulations at high numerical precisions. Our results may also apply to certain types of d-orbital transition-metal-oxides in solid state systems such as the LaAlO3/SrTiO3 interface.

1) Congjun Wu, "Unconventional Bose-Einstein Condensations Beyond the

No-node'' Theorem" Mod. Phys. Lett. 23, 1 (2009), a brief review.
2)  Yi Li, E. H. Lieb, Congjun Wu, Exact Results on Itinerant Ferromagnetism in Multi-orbital Systems on Square and Cubic Lattices Phys. Rev. Lett. 112, 217201(2014).

3) Shenglong Xu, Yi Li, Congjun Wu, Thermodynamic properties of a 2D itinerant ferromagnet - a sign-problem free quantum Monte Carlo study Phys. Rev. X 5, 021032, (2015).