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Infinite-randomness fixed points for chains of non-Abelian quasiparticles
1Department of Physics and National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32310, USA.
Physical Review Letters
|October 13, 2007
Summary
Non-Abelian quasiparticles in one-dimensional chains can form random singlet phases, mirroring ordinary spin chains. This provides a new description for the critical transverse field Ising model, revealing insights into quantum entanglement entropy scaling.
Area of Science:
- Condensed Matter Physics
- Quantum Field Theory
Background:
- One-dimensional systems with non-Abelian quasiparticles are described by SU(2)k Chern-Simons-Witten theory.
- These systems can exhibit random singlet phases, similar to those found in disordered spin chains.
Purpose of the Study:
- To explore the random singlet phases of one-dimensional non-Abelian quasiparticles.
- To connect these phases to the critical transverse field Ising model.
- To analyze the entanglement entropy scaling in these phases.
Main Methods:
- Utilizing SU(2)k Chern-Simons-Witten theory to model one-dimensional non-Abelian quasiparticles.
- Establishing an analogy between these quasiparticle chains and random chains of ordinary spin-1/2 particles.
- Investigating the specific case of k=2 to describe the infinite-randomness fixed point of the critical transverse field Ising model.
Main Results:
- One-dimensional non-Abelian quasiparticle chains can enter random singlet phases.
- For k=2, this phase offers a random singlet description of the critical transverse field Ising model's infinite-randomness fixed point.
- Entanglement entropy S(L) for a region of size L scales as S(L) ~ (ln d)/3 log(2)L for large L.
Conclusions:
- The study establishes a connection between non-Abelian quasiparticles and random singlet phases.
- The findings provide a novel perspective on the critical transverse field Ising model.
- The derived entanglement entropy scaling offers a key characteristic of these quantum phases.
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