  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.
