Liquids in multiorbital SU(N) magnets made up of ultracold alkaline-earth atoms

In this work we study one family of liquid states of k-orbital SU(N) spin systems, focusing on the case of k=2 which can be realized by ultracold alkaline-earth atoms trapped in optical lattices, with N as large as 10. Five different algebraic liquid states with selectively coupled charge, spin, and orbital quantum fluctuations are considered. The algebraic liquid states can be stabilized with large enough N and the scaling dimension of physical order parameters is calculated using a systematic 1/N expansion. The phase transitions between these liquid states are also studied and all the algebraic liquid states discussed in this work can be obtained from one mother state with SU(2) x U(1) gauge symmetry.