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Atomically Traceable Nanostructure Fabrication
Published on: July 17, 2015
Interacting anyons in topological quantum liquids: the golden chain
Adrian Feiguin1, Simon Trebst, Andreas W W Ludwig
1Microsoft Research, Station Q, University of California, Santa Barbara, California 93106, USA.
Physical Review Letters
|May 16, 2007
Summary
This study explores quantum spin Hamiltonians using anyonic degrees of freedom. A critical model of Fibonacci anyons exhibits a dynamical critical exponent of z=1, linked to a 2D conformal field theory.
Area of Science:
- Condensed Matter Physics
- Quantum Information Theory
- Topological Quantum Computation
Background:
- Generalizations of quantum spin Hamiltonians are explored.
- Anyonic degrees of freedom offer a novel approach to quantum systems.
- The quantum Heisenberg model serves as an analogy for interacting anyons.
Purpose of the Study:
- To investigate a model of interacting anyons analogous to quantum spin systems.
- To determine the critical properties and theoretical description of a Fibonacci anyon chain.
- To establish the topological origin of the model's gaplessness.
Main Methods:
- Numerical simulations of a chain of Fibonacci anyons.
- Analysis using two-dimensional (2D) conformal field theory.
- Exact mapping to the 2D tricritical Ising model via the restricted-solid-on-solid representation of the Temperley-Lieb algebra.
Main Results:
- The Fibonacci anyon chain model is found to be critical.
- A dynamical critical exponent z=1 is identified.
- The system is described by a 2D conformal field theory with central charge c=7/10.
- An exact mapping to the 2D tricritical Ising model is established.
Conclusions:
- The gaplessness of the anyonic chain has a topological origin.
- The study provides a precise theoretical framework for interacting anyons.
- This work bridges concepts from condensed matter physics and quantum field theory.
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