We report on a phenomenological study of superfluid to Mott insulator transitions of bosons on the triangular lattice, focusing primarily on the interplay between Mott localization and geometrical charge frustration at
1∕2-filling. A general dual-vortex field theory is developed for arbitrary rational filling factors
f, based on the appropriate projective symmetry group. At the simple nonfrustrated density
f=1∕3, we uncover an example of a deconfined quantum critical point very similar to that found on the half-filled square lattice. Turning to
f=1∕2, the behavior is quite different. Here, we find that the low-energy action describing the Mott transition has an emergent non-Abelian $SU(2)\ifmmode\times\else\texttimes\fi{}U(1)$ symmetry, which is not present at the microscopic level. This large non-Abelian symmetry is directly related to the frustration-induced quasidegeneracy between many charge-ordered states not related by microscopic symmetries. Through this ``pseudospin''
SU(2) symmetry, the charged excitations in the insulator close to the Mott transition develop a Skyrmion-like character. This leads to an understanding of the supersolid phase of the triangular lattice
XXZ model as a ``partially melted'' Mott insulator, for more information see Melko et al. [Phys. Rev. Lett. 95, 127207 (2005)], Heidarian and Damle [Phys. Rev. Lett. 95, 127206 (2005)], and Wessel and Troyer [Phys. Rev. Lett. 95, 127205 (2005)]. The latter picture naturally explains a number of puzzling numerical observations of the properties of this supersolid. Moreover, we predict that the nearby quantum phase transition from this supersolid to the Mott insulator is in the noncompact
CP1 critical universality class as presented in Motrunich and Vishwanath [Phys. Rev. B. 70, 075104 (2004)]. A description of a broad range of other Mott and supersolid states, and a diverse set of quantum critical points between them, is also provided.
The spontaneously broken of translational symmetry is usually due to the competition between local interactions and long-range interactions. However, in this paper, we show how a crystalline order can be generated by the competition between local interaction and long-range correlation by frustration. Here we propose a positive hopping Bose Hubbard model on triangle lattices with a pair creation term which comes from frustrated linked cavity arrays with degenerate quantum gases in them. We find by increasing the strength of pair creation term against local interaction strength, two kinds of density wave ordered superradiant photonic fluid phase can be realized and a first order transition between two different density wave ordered states is found. This proposal shows us a new way to produce coherent "solid" phase without the help of long range interactions.
Abstract The combination of strong correlation and emergent lattice can be achieved when quantum gases are confined in a superradiant Fabry–Perot cavity. In addition to the discoveries of exotic phases, such as density wave ordered Mott insulator and superfluid, a surprising kink structure is found in the slope of the cavity strength as a function of the pumping strength. In this article, we show that the appearance of such a kink is a manifestation of a liquid–vapour-like transition between two superfluids with different densities. The slopes in the immediate neighborhood of the kink become divergent at the liquid–vapour critical points and display a critical scaling law with a critical exponent 1 in the quantum critical region.
We describe the localization transition of superfluids on two-dimensional lattices into commensurate Mott insulators with average particle density
p∕q (
p,q relatively prime integers) per lattice site. For bosons on the square lattice, we argue that the superfluid has at least
q degenerate species of vortices which transform under a projective representation of the square-lattice space group (a PSG). The formation of a single-vortex condensate produces the Mott insulator, which is required by the PSG to have density wave order at wavelengths of
q∕n lattice sites (
n integer) along the principle axes; such a second-order transition is forbidden in the Landau-Ginzburg-Wilson frame-work. We also discuss the superfluid-insulator transition in the direct boson representation and find that an interpretation of the quantum criticality in terms of deconfined fractionalized bosons is only permitted at special values of
q for which a permutative representation of the PSG exists. We argue [and demonstrate in detail in a companion paper: L. Balents et al., following paper, Phys. Rev. B 71, 144509 (2005)] that our results apply essentially unchanged to electronic systems with short-range pairing, with the PSG determined by the particle density of Cooper pairs. We also describe the effect of static impurities in the superfluid: the impurities locally break the degeneracy between the
q vortex species, and this induces density-wave order near each vortex. We suggest that such a theory offers an appealing rationale for the local density-of-states modulations observed by Hoffman et al. [Science 295, 466 (2002)], in scanning tunneling microscopy (STM) studies of the vortex lattice of ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ and allows a unified description of the nucleation of density-wave order in zero and finite magnetic fields. We note signatures of our theory that may be tested by future STM experiments.
We present a detailed study of the Bose-Hubbard model in a
p-band triangular lattice by focusing on the evolution of orbital order across the superfluid-Mott insulator transition. Two distinct phases are found in the superfluid regime. One of these phases adiabatically connects the weak interacting limit. This phase is characterized by the intertwining of axial ${p}_{\ifmmode\pm\else\textpm\fi{}}={p}_{x}\ifmmode\pm\else\textpm\fi{}i{p}_{y}$ and in-plane ${p}_{\ensuremath{\theta}}=cos\ensuremath{\theta}{p}_{x}+sin\ensuremath{\theta}{p}_{y}$ orbital orders, which break the time-reversal symmetry and lattice symmetries simultaneously. In addition, the calculated Bogoliubov excitation spectrum gaps the original Dirac points in the single-particle spectrum but exhibits emergent Dirac points. The other superfluid phase in close proximity to the Mott insulator with unit boson filling shows a detwined in-plane ferro-orbital order. Finally, an orbital exchange model is constructed for the Mott insulator phase. Its classical ground state has an emergent
SO(2) rotational symmetry in the in-plane orbital space and therefore enjoys an infinite degeneracy, which is ultimately lifted by the orbital fluctuation via the order by disorder mechanism. Our systematic analysis suggests that the in-plane ferro-orbital order in the Mott insulator phase agrees with and likely evolves from the latter superfluid phase.
The study of geometrically frustrated many-body quantum systems is of central importance to uncover novel quantum mechanical effects. We design a scheme where ultracold bosons trapped in a one-dimensional state-dependent optical lattice are modeled by a frustrated Bose-Hubbard Hamiltonian. A derivation of the Hamiltonian parameters based on Cesium atoms, further show large tunability of contact and nearest-neighbor interactions. For pure contact repulsion, we discover the presence of two phases peculiar to frustrated quantum magnets: the bond-order-wave insulator with broken inversion symmetry and a chiral superfluid. When the nearest-neighbor repulsion becomes sizable, a further density-wave insulator with broken translational symmetry can appear. We show that the phase transition between the two spontaneously symmetry-broken phases is continuous, thus representing a one-dimensional deconfined quantum critical point not captured by the Landau-Ginzburg-Wilson symmetry-breaking paradigm. Our results provide a solid ground to unveil the novel quantum physics induced by the interplay of nonlocal interactions, geometrical frustration, and quantum fluctuations.