39 research outputs found
Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Super-Geometry
Recent vigorous investigations of topological order have not only discovered
new topological states of matter but also shed new light to "already known"
topological states. One established example with topological order is the
valence bond solid (VBS) states in quantum antiferromagnets. The VBS states are
disordered spin liquids with no spontaneous symmetry breaking but most
typically manifest topological order known as hidden string order on 1D chain.
Interestingly, the VBS models are based on mathematics analogous to fuzzy
geometry. We review applications of the mathematics of fuzzy super-geometry in
the construction of supersymmetric versions of VBS (SVBS) states, and give a
pedagogical introduction of SVBS models and their properties [arXiv:0809.4885,
1105.3529, 1210.0299]. As concrete examples, we present detail analysis of
supersymmetric versions of SU(2) and SO(5) VBS states, i.e. UOSp(N|2) and
UOSp(N|4) SVBS states whose mathematics are closely related to fuzzy two- and
four-superspheres. The SVBS states are physically interpreted as hole-doped VBS
states with superconducting property that interpolate various VBS states
depending on value of a hole-doping parameter. The parent Hamiltonians for SVBS
states are explicitly constructed, and their gapped excitations are derived
within the single-mode approximation on 1D SVBS chains. Prominent features of
the SVBS chains are discussed in detail, such as a generalized string order
parameter and entanglement spectra. It is realized that the entanglement
spectra are at least doubly degenerate regardless of the parity of bulk
(super)spins. Stability of topological phase with supersymmetry is discussed
with emphasis on its relation to particular edge (super)spin states.Comment: Review article, 1+104 pages, 37 figures, published versio
Ferromagnetism in the SU(N) Kondo lattice model -- SU(N) double exchange and supersymmetry
We study the ground-state properties of the SU(N)-generalization of the
Kondo-lattice model in one dimension when the Kondo coupling J_K (both
ferromagnetic and antiferromagnetic) is sufficiently strong. Both cases can be
realized using alkaline-earth-like cold gases in optical lattices.
Specifically, we first carry out the strong-coupling expansion and identify two
insulating phases (one of which is the SU(N)-analogue of the well-known gapped
Kondo singlet phase). We then rigorously establish that the ground state in the
low-density (for J_K0) region is
ferromagnetic. The results are accounted for by generalizing the
double-exchange mechanism to SU(N) "spins". Possible realizations of Bose-Fermi
supersymmetry SU(N|1) in the (generalized) SU(N) Kondo-lattice model are
discussed as well.Comment: 21 pages, 13 figures, final versio