Topological entropy in physics | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-29

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Topological_entropy_in_physics


00:02:03 1 See also
00:02:07 2 References



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SUMMARY
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The topological entanglement entropy[1] [2] or topological entropy, usually denoted by γ, is a number characterizing many-body states that possess topological order.
A non-zero topological entanglement entropy reflects the presence of long range quantum entanglements in a many-body quantum state. So the  topological entanglement entropy links topological order with pattern of 
long range quantum entanglements.
Given a topologically ordered state, the topological entropy can be extracted from the asymptotic behavior of the Von Neumann entropy measuring the quantum entanglement between a spatial block and the rest of the system.  The entanglement entropy of a simply connected region of boundary length L, within an infinite two-dimensional topologically ordered state, has the following form for large L:

  
    
      
        
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    {\displaystyle S_{L}\;\longrightarrow \;\alpha L-\gamma +{\mathcal {O}}(L^{-\nu })\;,\qquad \nu 0\,\!}
  -γ is the topological entanglement entropy.
The topological entanglement entropy is equal to the logarithm of the total quantum dimension of the quasiparticle excitations of the state.  
For example, the simplest fractional quantum Hall states, the Laughlin states at filling fraction 1/m, have γ = ½log(m).  The Z2 fractionalized states, such as topologically ordered states of 
Z2 spin-liquid, quantum dimer models on non-bipartite lattices, and Kitaev's toric code state, are characterized γ = log(2).