3,440 research outputs found
Matrix product states for anyonic systems and efficient simulation of dynamics
Matrix product states (MPS) have proven to be a very successful tool to study
lattice systems with local degrees of freedom such as spins or bosons.
Topologically ordered systems can support anyonic particles which are labeled
by conserved topological charges and collectively carry non-local degrees of
freedom. In this paper we extend the formalism of MPS to lattice systems of
anyons. The anyonic MPS is constructed from tensors that explicitly conserve
topological charge. We describe how to adapt the time-evolving block decimation
(TEBD) algorithm to the anyonic MPS in order to simulate dynamics under a local
and charge-conserving Hamiltonian. To demonstrate the effectiveness of anyonic
TEBD algorithm, we used it to simulate (i) the ground state (using imaginary
time evolution) of an infinite 1D critical system of (a) Ising anyons and (b)
Fibonacci anyons both of which are well studied, and (ii) the real time
dynamics of an anyonic Hubbard-like model of a single Ising anyon hopping on a
ladder geometry with an anyonic flux threading each island of the ladder. Our
results pertaining to (ii) give insight into the transport properties of
anyons. The anyonic MPS formalism can be readily adapted to study systems with
conserved symmetry charges, as this is equivalent to a specialization of the
more general anyonic case.Comment: 18 pages, 15 figue
Infinite Randomness Phases and Entanglement Entropy of the Disordered Golden Chain
Topological insulators supporting non-abelian anyonic excitations are at the
center of attention as candidates for topological quantum computation. In this
paper, we analyze the ground-state properties of disordered non-abelian anyonic
chains. The resemblance of fusion rules of non-abelian anyons and real space
decimation strongly suggests that disordered chains of such anyons generically
exhibit infinite-randomness phases. Concentrating on the disordered golden
chain model with nearest-neighbor coupling, we show that Fibonacci anyons with
the fusion rule exhibit two
infinite-randomness phases: a random-singlet phase when all bonds prefer the
trivial fusion channel, and a mixed phase which occurs whenever a finite
density of bonds prefers the fusion channel. Real space RG analysis
shows that the random-singlet fixed point is unstable to the mixed fixed point.
By analyzing the entanglement entropy of the mixed phase, we find its effective
central charge, and find that it increases along the RG flow from the random
singlet point, thus ruling out a c-theorem for the effective central charge.Comment: 16 page
Geometrical approach to SU(2) navigation with Fibonacci anyons
Topological quantum computation with Fibonacci anyons relies on the
possibility of efficiently generating unitary transformations upon
pseudoparticles braiding. The crucial fact that such set of braids has a dense
image in the unitary operations space is well known; in addition, the
Solovay-Kitaev algorithm allows to approach a given unitary operation to any
desired accuracy. In this paper, the latter task is fulfilled with an
alternative method, in the SU(2) case, based on a generalization of the
geodesic dome construction to higher dimension.Comment: 12 pages, 5 figure
Towards a dynamic rule-based business process
IJWGS is now included in Science Citation Index Expanded (SCIE), starting from volume 4, 2008. The first impact factor, which will be for 2010, is expected to be published in mid 201
Simulation of anyons with tensor network algorithms
Interacting systems of anyons pose a unique challenge to condensed matter
simulations due to their non-trivial exchange statistics. These systems are of
great interest as they have the potential for robust universal quantum
computation, but numerical tools for studying them are as yet limited. We show
how existing tensor network algorithms may be adapted for use with systems of
anyons, and demonstrate this process for the 1-D Multi-scale Entanglement
Renormalisation Ansatz (MERA). We apply the MERA to infinite chains of
interacting Fibonacci anyons, computing their scaling dimensions and local
scaling operators. The scaling dimensions obtained are seen to be in agreement
with conformal field theory. The techniques developed are applicable to any
tensor network algorithm, and the ability to adapt these ansaetze for use on
anyonic systems opens the door for numerical simulation of large systems of
free and interacting anyons in one and two dimensions.Comment: Fixed typos, matches published version. 16 pages, 21 figures, 4
tables, RevTeX 4-1. For a related work, see arXiv:1006.247
Genetic braid optimization: A heuristic approach to compute quasiparticle braids
In topologically-protected quantum computation, quantum gates can be carried
out by adiabatically braiding two-dimensional quasiparticles, reminiscent of
entangled world lines. Bonesteel et al. [Phys. Rev. Lett. 95, 140503 (2005)],
as well as Leijnse and Flensberg [Phys. Rev. B 86, 104511 (2012)] recently
provided schemes for computing quantum gates from quasiparticle braids.
Mathematically, the problem of executing a gate becomes that of finding a
product of the generators (matrices) in that set that approximates the gate
best, up to an error. To date, efficient methods to compute these gates only
strive to optimize for accuracy. We explore the possibility of using a generic
approach applicable to a variety of braiding problems based on evolutionary
(genetic) algorithms. The method efficiently finds optimal braids while
allowing the user to optimize for the relative utilities of accuracy and/or
length. Furthermore, when optimizing for error only, the method can quickly
produce efficient braids.Comment: 6 pages 4 figure
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