23 citations · 147 across the 17 of their papers we have counts for
17 papers
Temperley-Lieb and Birman-Murakami-Wenzl like relations from multiplicity free semi-simple tensor system
Peter E. Finch
In this article we consider conditions under which projection operators in multiplicity free semi-simple tensor categories satisfy Temperley-Lieb like relations. This is then used…
clock models and chains of non-Abelian anyons: symmetries, integrable points and low energy properties
Peter E. Finch, Michael Flohr, Holger Frahm
We study two families of quantum models which have been used previously to investigate the effect of topological symmetries in one-dimensional correlated matter. Various striking s…
Classification of Metaplectic Fusion Categories
Eddy Ardonne, Peter E. Finch, Matthew Titsworth
In this paper, we study a family of fusion and modular systems realizing fusion categories Grothendieck equivalent to the representation category for . These categories…
From tensor category to Temperley-Lieb algebra representation
Peter E. Finch, Zoltan Kadar, Paul Martin
We construct a representation of the Temperley-Lieb algebra from a multiplicity-free semisimple monoidal Abelian category , with two simple objects and such that…
Exact solution of the non-Abelian anyon chain
Natalia Braylovskaya, Peter E. Finch, Holger Frahm
Commuting transfer matrices for linear chains of interacting non-Abelian anyons from the two-dimensional irreducible representation of the dihedral group (or, equivalently, t…
Theta function solutions of the qKZB equation for a face model
Peter E. Finch, Robert Weston, Paul Zinn-Justin
We consider the quantum Knizhnik-Zamolodchikov-Bernard equation for a face model with elliptic weights, the SOS model. We provide explicit solutions as theta functions. On the so-c…
Induced topological order at the boundary of 3D topological superconductors
Peter Finch, James de Lisle, Giandomenico Palumbo +1
We present tight-binding models of 3D topological superconductors in class DIII that support a variety of winding numbers. We show that gapless Majorana surface states emerge at th…
Integrable anyon chains: from fusion rules to face models to effective field theories
Peter E. Finch, Michael Flohr, Holger Frahm
Starting from the fusion rules for the algebra we construct one-dimensional lattice models of interacting anyons with commuting transfer matrices of `interactions round t…
Quantum phases of a chain of strongly interacting anyons
Peter E. Finch, Holger Frahm, Marius Lewerenz +2
We study a strongly interacting chain of anyons with fusion rules determined by SO(5)2. The phase portrait is identified with a combination of numerical and analytical techniques.…
The -anyon chain: integrable boundary conditions and excitation spectra
Peter E. Finch, Holger Frahm
Chains of interacting non-Abelian anyons with local interactions invariant under the action of the Drinfeld double of the dihedral group are constructed. Formulated as a spin…
From spin to anyon notation: The XXZ Heisenberg model as a (or ) anyon chain
Peter E. Finch
We discuss a relationship between certain one-dimensional quantum spin chains and anyon chains. In particular we show how the XXZ Heisenberg chain is realised as a (alterna…
Collective states of interacting non-Abelian anyons
Peter E. Finch, Holger Frahm
We study the finite size spectrum of integrable quantum chains of interacting non-Abelian anyons constructed using the Drinfeld double of the dihedral group . The gapless low…
Integrable Hamiltonians with symmetry from the Fateev-Zamolodchikov model
P. E. Finch
A special case of the Fateev-Zamolodchikov model is studied resulting in a solution of the Yang-Baxter equation with two spectral parameters. Integrable models from this solution a…
Ground-state phase diagram for a system of interacting, non-Abelian anyons
P. E. Finch, H. Frahm, J. Links
We study an exactly solvable model of non-Abelian anyons on a one-dimensional lattice with a free coupling parameter in the Hamiltonian. For certain values of the coupling…
Solutions of the Yang-Baxter equation: descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras
P. E. Finch, K. A. Dancer, P. S. Isaac +1
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 mod…
Integrable boundary conditions for a non-abelian anyon chain with symmetry
K. A. Dancer, P. E. Finch, P. S. Isaac +1
A general formulation of the Boundary Quantum Inverse Scattering Method is given which is applicable in cases where -matrix solutions of the Yang--Baxter equation do not have th…
Universal Baxterization for -graded Hopf algebras
K. A. Dancer, P. E. Finch, P. S. Isaac
We present a method for Baxterizing solutions of the constant Yang-Baxter equation associated with -graded Hopf algebras. To demonstrate the approach, we provide exampl…