3,533 research outputs found
Representations of the quantum doubles of finite group algebras and solutions of the Yang--Baxter equation
Quantum doubles of finite group algebras form a class of quasi-triangular
Hopf algebras which algebraically solve the Yang--Baxter equation. Each
representation of the quantum double then gives a matrix solution of the
Yang--Baxter equation. Such solutions do not depend on a spectral parameter,
and to date there has been little investigation into extending these solutions
such that they do depend on a spectral parameter. Here we first explicitly
construct the matrix elements of the generators for all irreducible
representations of quantum doubles of the dihedral groups . These results
may be used to determine constant solutions of the Yang--Baxter equation. We
then discuss Baxterisation ans\"atze to obtain solutions of the Yang--Baxter
equation with spectral parameter and give several examples, including a new
21-vertex model. We also describe this approach in terms of minimal-dimensional
representations of the quantum doubles of the alternating group and the
symmetric group .Comment: 19 pages, no figures, changed introduction, added reference
Solutions of the Yang-Baxter equation: descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras
The representation theory of the Drinfeld doubles of dihedral groups is used
to solve the Yang-Baxter equation. Use of the 2-dimensional representations
recovers the six-vertex model solution. Solutions in arbitrary dimensions,
which are viewed as descendants of the six-vertex model case, are then obtained
using tensor product graph methods which were originally formulated for quantum
algebras. Connections with the Fateev-Zamolodchikov model are discussed.Comment: 34 pages, 2 figure
Bethe ansatz solution of an integrable, non-Abelian anyon chain with D(D_3) symmetry
The exact solution for the energy spectrum of a one-dimensional Hamiltonian
with local two-site interactions and periodic boundary conditions is
determined. The two-site Hamiltonians commute with the symmetry algebra given
by the Drinfeld double D(D_3) of the dihedral group D_3. As such the model
describes local interactions between non-Abelian anyons, with fusion rules
given by the tensor product decompositions of the irreducible representations
of D(D_3). The Bethe ansatz equations which characterise the exact solution are
found through the use of functional relations satisfied by a set of mutually
commuting transfer matrices.Comment: 19 page
Universal Baxterization for -graded Hopf algebras
We present a method for Baxterizing solutions of the constant Yang-Baxter
equation associated with -graded Hopf algebras. To demonstrate the
approach, we provide examples for the Taft algebras and the quantum group
.Comment: 8 page
Patient-Reported Outcomes following Single- and Multiple-Radius Total Knee Replacement: A Randomized, Controlled Trial
Although single-radius (SR) designs of total knee replacement (TKR) have theoretical benefits, the clinical advantage conferred by such designs is unknown. The aim of this randomized, controlled study was to compare the short-term clinical outcomes of the two design rationales. A total of 105 knees were randomized to receive either a single radius (Scorpio, Stryker; SR Group) or multiple radius (AGC, Zimmer Biomet; MR group) TKR. Patient-reported outcomes (Oxford Knee Score [OKS] and Knee Society Score [KSS]) were collected at 6 weeks, 6 months, and 1 year following surgery. No knees were revised. There was no difference in primary outcomes: OKS was 39.5 (95% confidence interval [CI]: 36.9–42.1) in the SR group and 38.1 (95% CI: 36.0–40.3) in the MR group (p = 0.40). KSS was 168.4 (95% CI: 159.8–177.0) in the SR group; 159.5 (95% CI 150.5–168.5) in the MR group (p = 0.16). There was a small but statistically significant difference in the degree of change of the objective subscale of the KSS, favoring the SR design (p = 0.04), but this is of uncertain clinical relevance. The reported benefits of SR designs do not provide demonstrable functional advantages in the short term
Framework for classifying logical operators in stabilizer codes
Entanglement, as studied in quantum information science, and non-local
quantum correlations, as studied in condensed matter physics, are fundamentally
akin to each other. However, their relationship is often hard to quantify due
to the lack of a general approach to study both on the same footing. In
particular, while entanglement and non-local correlations are properties of
states, both arise from symmetries of global operators that commute with the
system Hamiltonian. Here, we introduce a framework for completely classifying
the local and non-local properties of all such global operators, given the
Hamiltonian and a bi-partitioning of the system. This framework is limited to
descriptions based on stabilizer quantum codes, but may be generalized. We
illustrate the use of this framework to study entanglement and non-local
correlations by analyzing global symmetries in topological order, distribution
of entanglement and entanglement entropy.Comment: 20 pages, 9 figure
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