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Liquids in multi-orbital SU(N) Magnets with 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.