88 research outputs found
Topological phases and phase transitions on the square-octagon lattice
We theoretically investigate a tight binding model of fermions hopping on the
square-octagon lattice which consists of a square lattice with plaquette
corners themselves decorated by squares. Upon the inclusion of second neighbor
spin-orbit coupling or non-Abelian gauge fields, time-reversal symmetric
topological Z_2 band insulators are realized. Additional insulating and gapless
phases are also realized via the non-Abelian gauge fields. Some of the phase
transitions involve topological changes to the Fermi surface. The stability of
the topological phases to various symmetry breaking terms is investigated via
the entanglement spectrum. Our results enlarge the number of known exactly
solvable models of Z_2 band insulators, and are potentially relevant to the
realization and identification of topological phases in both the solid state
and cold atomic gases.Comment: 12 pages, 9 figure
Interacting Anyonic Fermions in a Two-Body Color Code Model
We introduce a two-body quantum Hamiltonian model of spin-1/2 on a 2D spatial
lattice with exact topological degeneracy in all coupling regimes. There exists
a gapped phase in which the low-energy sector reproduces an effective color
code model. High energy excitations fall into three families of anyonic
fermions that turn out to be strongly interacting. The model exhibits a Z_2xZ_2
gauge group symmetry and string-net integrals of motion, which are related to
the existence of topological charges that are invisible to moving high-energy
fermions.Comment: RevTeX 4, 2 figures, longer versio
Unusual magnetic phases in the strong interaction limit of two-dimensional topological band insulators in transition metal oxides
The expected phenomenology of non-interacting topological band insulators
(TBI) is now largely theoretically understood. However, the fate of TBIs in the
presence of interactions remains an active area of research with novel,
interaction-driven topological states possible, as well as new exotic magnetic
states. In this work we study the magnetic phases of an exchange Hamiltonian
arising in the strong interaction limit of a Hubbard model on the honeycomb
lattice whose non-interacting limit is a two-dimensional TBI recently proposed
for the layered heavy transition metal oxide compound, (Li,Na)IrO. By a
combination of analytical methods and exact diagonalization studies on finite
size clusters, we map out the magnetic phase diagram of the model. We find that
strong spin-orbit coupling can lead to a phase transition from an
antiferromagnetic Ne\'el state to a spiral or stripy ordered state. We also
discuss the conditions under which a quantum spin liquid may appear in our
model, and we compare our results with the different but related
Kitaev-Heisenberg-- model which has recently been studied in a
similar context.Comment: 12 pages, 8 figure
Quantum phase transitions in the Kondo-necklace model: Perturbative continuous unitary transformation approach
The Kondo-necklace model can describe magnetic low-energy limit of strongly
correlated heavy fermion materials. There exist multiple energy scales in this
model corresponding to each phase of the system. Here, we study quantum phase
transition between the Kondo-singlet phase and the antiferromagnetic long-range
ordered phase, and show the effect of anisotropies in terms of quantum
information properties and vanishing energy gap. We employ the "perturbative
continuous unitary transformations" approach to calculate the energy gap and
spin-spin correlations for the model in the thermodynamic limit of one, two,
and three spatial dimensions as well as for spin ladders. In particular, we
show that the method, although being perturbative, can predict the expected
quantum critical point, where the gap of low-energy spectrum vanishes, which is
in good agreement with results of other numerical and Green's function
analyses. In addition, we employ concurrence, a bipartite entanglement measure,
to study the criticality of the model. Absence of singularities in the
derivative of concurrence in two and three dimensions in the Kondo-necklace
model shows that this model features multipartite entanglement. We also discuss
crossover from the one-dimensional to the two-dimensional model via the ladder
structure.Comment: 12 pages, 6 figure
Doping the Kane-Mele-Hubbard model: A Slave-Boson Approach
We study the Kane-Mele-Hubbard model both at half-filling and away from
half-filling using a slave-boson mean-field approach at zero temperature. We
obtain a phase diagram at half-filling and discuss its connection to recent
results from quantum Monte Carlo, slave-rotor, and mean-field studies. In
particular, we find a small window in parameter space where a spin liquid phase
with gapped spin and charge excitations reside. Upon doping, we show the spin
liquid state becomes a superconducting state by explicitly calculating the
singlet pairing order parameters. Interestingly, we find an "optimal" doping
for such superconductivity. Our work reveals some of the phenomenology
associated with doping an interacting system with strong spin-orbit coupling.Comment: 11 pages and 9 figure
Topological insulators and fractional quantum Hall effect on the ruby lattice
We study a tight-binding model on the two-dimensional ruby lattice. This
lattice supports several types of first and second neighbor spin-dependent
hopping parameters in an -band model that preserves time-reversal symmetry.
We discuss the phase diagram of this model for various values of the hopping
parameters and filling fractions, and note an interesting competition between
spin-orbit terms that individually would drive the system to a
topological insulating phase. We also discuss a closely related spin-polarized
model with only first and second neighbor hoppings and show that extremely flat
bands with finite Chern numbers result, with a ratio of the band gap to the
band width approximately 70. Such flat bands are an ideal platform to realize a
fractional quantum Hall effect at appropriate filling fractions. The ruby
lattice can be possibly engineered in optical lattices, and may open the door
to studies of transitions between quantum spin liquids, topological insulators,
and integer and fractional quantum Hall states.Comment: 9 pages, 8 figures, updated figures, updated references, updated
acknowledgement, some details in calculation adde
Renormalization of concurrence: the application of quantum renormalization group to the quantum information systems
We have combined the idea of renormalization group and quantum information
theory. We have shown how the entanglement or concurrence evolve as the size of
the system being large, i.e. the finite size scaling is obtained. Moreover, It
introduces how the renormalization group approach can be implemented to obtain
the quantum information properties of a many body system. We have obtained the
concurrence as a measure of entanglement, its derivatives and their scaling
behavior versus the size of system for the one dimensional Ising model in
transverse field. We have found that the derivative of concurrence between two
blocks each containing half of the system size diverges at the critical point
with the exponent which is directly associated with the divergence of the
correlation length.Comment: 4 pages, 5 eps figure
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