Celebratio Mathematica — Freedman

Quantum computing

Works connected to Adrian Esteban Feiguin

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article M. Freedman, A. Feiguin, S. Trebst, A. Ludwig, M. Troyer, A. Kitaev, and Z. Wang: “Interacting anyons in topological quantum liquids: The golden chain,” Phys. Rev. Lett. 98 (2007), pp. 160409. ArXiv cond-mat/0612341

We discuss generalizations of quantum spin Hamiltonians using anyonic degrees of freedom. The simplest model for interacting anyons energetically favors neighboring anyons to fuse into the trivial (“identity”) channel, similar to the quantum Heisenberg model favoring neighboring spins to form spin singlets. Numerical simulations of a chain of Fibonacci anyons show that the model is critical with a dynamical critical exponent \( z=1 \), and described by a two-dimensional (\( 2D \)) conformal field theory with central charge \( c=7/10 \). An exact mapping of the anyonic chain onto the \( 2D \) tricritical Ising model is given using the restricted-solid-on-solid representation of the Temperley–Lieb algebra. The gaplessness of the chain is shown to have topological origin.

Zhenghan Wang	Related
Adrian Esteban Feiguin	Related
A. Ludwig	Related
Simon Trebst	Related
Matthias Troyer	Related
Alexei Kitaev	Related