5,247 research outputs found
Effect of Landau Level Mixing on Braiding Statistics
We examine the effect of Landau level mixing on the braiding statistics of
quasiparticles of abelian and nonabelian quantum Hall states. While path
dependent geometric phases can perturb the abelian part of the statistics, we
find that the nonabelian properties remain unchanged to an accuracy that is
exponentially small in the distance between quasiparticles.Comment: 4 page
Breaking of Particle-Hole Symmetry by Landau Level Mixing in the nu=5/2 Quantized Hall State
We perform numerical studies to determine if the fractional quantum Hall
state observed at filling nu=5/2 is the Moore-Read wavefunction or its particle
hole conjugate, the so-called AntiPfaffian. Using a truncated Hilbert space
approach we find that for realistic interactions, including Landau-level
mixing, the ground state remains fully polarized and the AntiPfaffian is
strongly favored.Comment: Main change is that the Anti-Pfaffian is favored instead of the
Pfaffian (caused by a sign error in the commutation relation of the dynamical
momenta). 4-plus pages, 3 figure
Exact Solutions of Fractional Chern Insulators: Interacting Particles in the Hofstadter Model at Finite Size
We show that all the bands of the Hofstadter model on the torus have an
exactly flat dispersion and Berry curvature when a special system size is
chosen. This result holds for any hopping and Chern number. Our analysis
therefore provides a simple rule for choosing a particularly advantageous
system size when designing a Hofstadter system whose size is controllable, like
a qubit lattice or an optical cavity array. The density operators projected
onto the flat bands obey exactly the Girvin-MacDonald-Platzman algebra, like
for Landau levels in the continuum in the case of , or obey its
straightforward generalization in the case of . This allows a mapping
between density-density interaction Hamiltonians for particles in the
Hofstatder model and in a continuum Landau level. By using the well-known
pseudopotential construction in the latter case, we obtain fractional Chern
insulator phases, the lattice counterpart of fractional quantum Hall phases,
that are exact zero-energy ground states of the Hofstadter model with certain
interactions. Finally, the addition of a harmonic trapping potential is shown
to lead to an appealingly symmetric description in which a new Hofstadter model
appears in momentum space.Comment: 15 pages, 8 figures; Published versio
3- and 4-body Interactions from 2-body interactions in Spin Models: A Route to Abelian and Non-Abelian Fractional Chern Insulators
We describe a method for engineering local -body interactions
() from two-body couplings in spin- systems. When implemented
in certain systems with a flat single-particle band with a unit Chern number,
the resulting many-body ground states are fractional Chern insulators which
exhibit abelian and non-abelian anyon excitations. The most complex of these,
with , has Fibonacci anyon excitations; our system is thus capable of
universal topological quantum computation. We then demonstrate that an
appropriately tuned circuit of qubits could faithfully replicate this model up
to small corrections, and further, we describe the process by which one might
create and manipulate non-abelian vortices in these circuits, allowing for
direct control of the system's quantum information content.Comment: 4 pages + references and supplemental informatio
Exactly Solvable Lattice Models with Crossing Symmetry
We show how to compute the exact partition function for lattice
statistical-mechanical models whose Boltzmann weights obey a special "crossing"
symmetry. The crossing symmetry equates partition functions on different
trivalent graphs, allowing a transformation to a graph where the partition
function is easily computed. The simplest example is counting the number of
nets without ends on the honeycomb lattice, including a weight per branching.
Other examples include an Ising model on the Kagome' lattice with three-spin
interactions, dimers on any graph of corner-sharing triangles, and non-crossing
loops on the honeycomb lattice, where multiple loops on each edge are allowed.
We give several methods for obtaining models with this crossing symmetry, one
utilizing discrete groups and another anyon fusion rules. We also present
results indicating that for models which deviate slightly from having crossing
symmetry, a real-space decimation (renormalization-group-like) procedure
restores the crossing symmetry
Size Constraints on Majorana Beamsplitter Interferometer: Majorana Coupling and Surface-Bulk Scattering
Topological insulator surfaces in proximity to superconductors have been
proposed as a way to produce Majorana fermions in condensed matter physics. One
of the simplest proposed experiments with such a system is Majorana
interferometry. Here, we consider two possibly conflicting constraints on the
size of such an interferometer. Coupling of a Majorana mode from the edge (the
arms) of the interferometer to vortices in the centre of the device sets a
lower bound on the size of the device. On the other hand, scattering to the
usually imperfectly insulating bulk sets an upper bound. From estimates of
experimental parameters, we find that typical samples may have no size window
in which the Majorana interferometer can operate, implying that a new
generation of more highly insulating samples must be explored.Comment: 14 pages, 6 figure
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