267 research outputs found

### 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.

### 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

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