Quantum phase transition in an array of coupled dissipative cavities

The features of superfluid-Mott insulator phase transition in the array of dissipative nonlinear cavities are analyzed. We show analytically that the coupling to the bath can be reduced to renormalizing the eigenmodes of atom-cavity system. This gives rise to a localizing effect and drives the system into mixed states. For the superfluid state, a dynamical instability will lead to a sweeping to a localized state of photons. For the Mott state, a dissipation-induced fluctuation will suppress the restoring of long-range phase coherence driven by interaction.

Classification of nematic order in 2+1D: Dislocation melting and $O(2)/Z_N$ lattice gauge theory

Nematic phases, breaking spontaneously rotational symmetry, provide for ubiquitously observed states of matter in both classical and quantum systems. These nematic states may be further classified by their $N$--fold rotational invariance described by cyclic groups $C_N$ in 2+1D. Starting from the space groups of underlying $2d$ crystals, we present a general classification scheme incorporating $C_N$ nematic phases that arise from dislocation-mediated melting and discuss the conventional tensor order parameters. By coupling the $O(2)$ matter fields to the $Z_N$ lattice gauge theory, an unified $O(2)/Z_N$ lattice gauge theory is constructed in order to describe all these nematic phases. This lattice gauge theory is shown to reproduce the $C_N$ nematic-isotropic liquid phase transitions and contains an additional deconfined phase. Finally, using our $O(2)/Z_N$ gauge theory framework, we discuss phase transitions between different $C_N$ nematics.

Extended dual description of Mott transition beyond two-dimensional space

Motivated by recent work of Mross and Senthil [Phys. Rev. B textbf{84}, 165126 (2011)] which provides a dual description for Mott transition from Fermi liquid to quantum spin liquid in two space dimensions, we extend their approach to higher dimensional cases, and we provide explicit formalism in three space dimensions. Instead of the vortices driving conventional Fermi liquid into quantum spin liquid states in 2D, it is the vortex lines to lead to the instability of Fermi liquid in 3D. The extended formalism can result in rich consequences when the vortex lines condense in different degrees of freedom. For example, when the vortex lines condense in charge phase degrees of freedom, the resulting effective fermionic action is found to be equivalent to that obtained by well-studied slave-particle approaches for Hubbard and/or Anderson lattice models, which confirm the validity of the extended dual formalism in 3D. When the vortex lines condense in spin phase degrees of freedom, a doublon metal with a spin gap and an instability to the unconventional superconducting pairing can be obtained. In addition, when the vortex lines condense in both phase degrees, an exotic doubled U(1) gauge theory occurs which describes a separation of spin-opposite fermionic excitations. It is noted that the first two features have been discussed in a similar way in 2D, the last one has not been reported in the previous works. The present work is expected to be useful in understanding the Mott transition happening beyond two space dimensions.