13 research outputs found
Topological semimetal in a fermionic optical lattice
Optical lattices play a versatile role in advancing our understanding of
correlated quantum matter. The recent implementation of orbital degrees of
freedom in chequerboard and hexagonal optical lattices opens up a new thrust
towards discovering novel quantum states of matter, which have no prior analogs
in solid state electronic materials. Here, we demonstrate that an exotic
topological semimetal emerges as a parity-protected gapless state in the
orbital bands of a two-dimensional fermionic optical lattice. The new quantum
state is characterized by a parabolic band-degeneracy point with Berry flux
, in sharp contrast to the flux of Dirac points as in graphene. We
prove that the appearance of this topological liquid is universal for all
lattices with D point group symmetry as long as orbitals with opposite
parities hybridize strongly with each other and the band degeneracy is
protected by odd parity. Turning on inter-particle repulsive interactions, the
system undergoes a phase transition to a topological insulator whose
experimental signature includes chiral gapless domain-wall modes, reminiscent
of quantum Hall edge states.Comment: 6 pages, 3 figures and Supplementary Informatio
Dzyaloshinskii-Moriya Interaction and Spiral Order in Spin-orbit Coupled Optical Lattices
We show that the recent experimental realization of spin-orbit coupling in
ultracold atomic gases can be used to study different types of spin spiral
order and resulting multiferroic effects. Spin-orbit coupling in optical
lattices can give rise to the Dzyaloshinskii-Moriya (DM) spin interaction which
is essential for spin spiral order. By taking into account spin-orbit coupling
and an external Zeeman field, we derive an effective spin model in the Mott
insulator regime at half filling and demonstrate that the DM interaction in
optical lattices can be made extremely strong with realistic experimental
parameters. The rich finite temperature phase diagrams of the effective spin
models for fermions and bosons are obtained via classical Monte Carlo
simulations.Comment: 7 pages, 5 figure
Quantum magnetism and criticality
Magnetic insulators have proved to be fertile ground for studying new types
of quantum many body states, and I survey recent experimental and theoretical
examples. The insights and methods transfer also to novel superconducting and
metallic states. Of particular interest are critical quantum states, sometimes
found at quantum phase transitions, which have gapless excitations with no
particle- or wave-like interpretation, and control a significant portion of the
finite temperature phase diagram. Remarkably, their theory is connected to
holographic descriptions of Hawking radiation from black holes.Comment: 39 pages, 10 figures, review article for non-specialists; (v2) added
clarifications and references; (v3) minor corrections; (v4) added footnote on
hydrodynamic long-time tail