Conventional description of Unconventional Coulomb-Crystal phase transitions in three-dimensional classical O(N) spin-ice

We study the phase transition between the high temperature Coulomb phase and the low temperature staggered crystal phase in three dimensional classical O(N) spin-ice model. Compared with the previously proposed CP(1) formalism on the Coulomb-crystal transition of the classical dimer model, our description based on constrained order parameter is more conventional, due to a fundamental difference between the O(N) and the dimer model. A systematic epsilon and 1/N expansion are used to study the universality class of the phase transition, and a stable fixed point is found based on our calculations for large enough N.Comment: 5 pages, 2 figure

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.Comment: 5 pages, 1 figur

Quantum Spin Hall, triplet Superconductor, and topological liquid on the honeycomb lattice

We classify the order parameters on the honeycomb lattice using the SO(4) symmetry of the Hubbard model. We will focus on the topologically nontrivial quantum spin Hall order and spin triplet superconductor, which together belong to the (3, 3) representation of the SO(4). Depending on the microscopic parameters, this (3, 3) order parameter has two types of ground states with different symmetries: type A, the ground state manifold is [S^2xS^2]/Z_2; and type B, with ground state manifold SO(3)xZ_2. We demonstrate that phase A is adjacent to a Z_2xZ_2 topological phase with mutual semion statistics between spin and charge excitations, while phase B is adjacent to a nonabelian phase described by SU(2) Chern-Simons theory. Connections of our study to the recent quantum Monte Carlo simulation on the Hubbard model on the honeycomb lattice will also be discussed.Comment: 9 pages, 3 figure

Low Energy Effective Field Theories of Sp(4) Spin systems

We study the classical and quantum phase transitions of Sp(4) spin systems on three dimensional stacked square and triangular lattices. We present general Ginzburg-Landau field theories for various types of Sp(4) spin orders with different ground state manifolds such as CP(3), S^7/Z_2, Grassmann manifold G_{2,5}, G_{2,6} and so on, based on which the nature of the classical phase transitions are studied, and a global phase diagram is presented. The classical phase transitions close to quantum phase transitions toward spin liquid states are also discussed based on renormalization group (RG) flow. Our results can be directly applied to the simplest Sp(4) and SU(4) Heisenberg models which can be realized using spin-3/2 atoms and Alkaline earth atoms trapped in optical lattice.Comment: 8 pages, 4 figure