Spin Liquid States on the Triangular and Kagome Lattices: A Projective Symmetry Group Analysis of Schwinger Boson States

A symmetry based analysis (Projective Symmetry Group) is used to study spin liquid phases on the triangular and Kagom\'e lattices in the Schwinger boson framework. A maximum of eight distinct $Z_2$ spin liquid states are found for each lattice, which preserve all symmetries. Out of these only a few have nonvanishing nearest neighbor amplitudes which are studied in greater detail. On the triangular lattice, only two such states are present - the first (zero-flux state) is the well known state introduced by Sachdev, which on condensation of spinons leads to the 120 degree ordered state. The other solution which we call the $\pi$-flux state has not previously been discussed. Spinon condensation leads to an ordering wavevector at the Brillouin zone edge centers, in contrast to the 120 degree state. While the zero-flux state is more stable with just nearest-neighbor exchange, we find that the introduction of either next-neighbor antiferromagnetic exchange or four spin ring-exchange (of the sign obtained from a Hubbard model) tends to favor the $\pi$-flux state. On the Kagom\'e lattice four solutions are obtained - two have been previously discussed by Sachdev, which on spinon condensation give rise to the $q=0$ and $\sqrt{3}\times\sqrt{3}$ spin ordered states. In addition we find two new states with significantly larger values of the quantum parameter at which magnetic ordering occurs. For one of them this even exceeds unity, $\kappa_c\approx 2.0$ in a nearest neighbor model, indicating that if stabilized, could remain spin disordered for physical values of the spin. This state is also stabilized by ring exchange interactions with signs as derived from the Hubbard model.Comment: revised, 21 pages, 19 figures, RevTex 4, corrected references, added 4 references, accepted by Phys.Rev.

Criterion for stability of Goldstone Modes and Fermi Liquid behavior in a metal with broken symmetry

There are few general physical principles that protect the low energy excitations of a quantum phase. Of these, Goldstone's theorem and Landau Fermi liquid theory are the most relevant to solids. We investigate the stability of the resulting gapless excitations - Nambu Goldstone bosons (NGBs) and Landau quasiparticles - when coupled to one another, which is of direct relevance to metals with a broken continuous symmetry. Typically, the coupling between NGBs and Landau quasiparticles vanishes at low energies leaving the gapless modes unaffected. If however the low energy coupling is non-vanishing, non-Fermi liquid behavior and overdamped bosons are expected. Here we prove a general criterion which specifies when the coupling is non-vanishing. It is satisfied by the case of a nematic Fermi fluid, consistent with earlier microscopic calculations. In addition, the criterion identifies a new kind of symmetry breaking - of magnetic translations - where non-vanishing couplings should arise, opening a new route to realizing non-Fermi liquid phases.Comment: 6 pages + 10 pages (Supplemental Material), 3 + 2 figures; v2:revised for clarit

Spin phonon induced colinear order and magnetization plateaus in triangular and kagome antiferromagnets. Applications to CuFeO_2

Coupling between spin and lattice degrees of freedom are important in geometrically frustrated magnets where they can lead to degeneracy lifting and novel orders. We show that moderate spin-lattice couplings in triangular and Kagome antiferromagnets can induce complex colinear magnetic orders. When classical Heisenberg spins on the triangular lattice are coupled to Einstein phonons, a rich variety of phases emerge, including the experimentally observed four sublattice state and the five sublattice 1/5th plateau state seen in the magneto-electric material CuFeO$_2$. In addition we predict magnetization plateaus at 1/3, 3/7, 1/2, 3/5 and 5/7 at these couplings. Strong spin-lattice couplings induce a striped colinear state, seen in $\alpha$-NaFeO$_2$ and MnBr$_2$. On the Kagome lattice, moderate spin-lattice couplings induce colinear order, but an extensive degeneracy remains.Comment: 5 pages, 4 figure

Flat band in twisted bilayer Bravais lattices

Band engineering in twisted bilayers of the five generic two-dimensional Bravais networks is demonstrated. We first derive symmetry-based constraints on the interlayer coupling, which helps us to predict and understand the shape of the potential barrier for the electrons under the influence of the moir\'{e} structure without reference to microscopic details. It is also pointed out that the generic constraints becomes best relevant when the typical length scale of the microscopic interlayer coupling is moderate. The concepts are numerically demonstrated in simple tight-binding models to show the band flattening due to the confinement into the potential profile fixed by the generic constraints. On the basis of the generic theory, we propose the possibility of anisotropic band flattening, in which quasi one-dimensional band dispersion is generated from relatively isotropic original band dispersion. In the strongly correlated regime, anisotropic band flattening leads to a spin-orbital model where intertwined magnetic and orbital ordering can give rise to rich physics.Comment: 10 page

Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect

We discuss physical properties of `integer' topological phases of bosons in D=3+1 dimensions, protected by internal symmetries like time reversal and/or charge conservation. These phases invoke interactions in a fundamental way but do not possess topological order and are bosonic analogs of free fermion topological insulators and superconductors. While a formal cohomology based classification of such states was recently discovered, their physical properties remain mysterious. Here we develop a field theoretic description of several of these states and show that they possess unusual surface states, which if gapped, must either break the underlying symmetry, or develop topological order. In the latter case, symmetries are implemented in a way that is forbidden in a strictly two dimensional theory. While this is the usual fate of the surface states, exotic gapless states can also be realized. For example, tuning parameters can naturally lead to a deconfined quantum critical point or, in other situations, a fully symmetric vortex metal phase. We discuss cases where the topological phases are characterized by quantized magnetoelectric response \theta, which, somewhat surprisingly, is an odd multiple of 2\pi. Two different surface theories are shown to capture these phenomena - the first is a nonlinear sigma model with a topological term. The second invokes vortices on the surface that transform under a projective representation of the symmetry group. A bulk field theory consistent with these properties is identified, which is a multicomponent `BF' theory supplemented, crucially, with a topological term. A possible topological phase characterized by the thermal analog of the magnetoelectric effect is also discussed.Comment: 25 pages+ 3 pages Appendices, 3 figures. Introduction rewritten for clarity, minor technical changes and additional details of surface topological order adde