Quasiparticle statistics and braiding from ground state entanglement

By Yi Zhang, T. Grover, Ari M. Turner, M. Oshikawa, Ashvin Vishwanath. 2011

237 citations recorded by the source corpus.

Topologically ordered phases are gapped states, defined by the properties of excitations when taken around one another. Here we demonstrate a method to extract the statistics and braiding of excitations, given just the set of ground-state wave functions on a torus. This is achieved by studying the topological entanglement entropy (TEE) upon partitioning the torus into two cylinders. In this setting, general considerations dictate that the TEE generally differs from that in trivial partitions and depends on the chosen ground state. Central to our scheme is the identification of ground states with minimum entanglement entropy, which reflect the quasiparticle excitations of the topological phase. The transformation of these states allows for the determination of the modular S and U matrices which encode quasiparticle properties. We demonstrate our method by extracting the modular S matrix of a chiral spin liquid phase using a Monte Carlo scheme to calculate the TEE and prove that the quasiparticles obey semionic statistics. This method offers a route to nearly complete determination of the topological order in certain cases.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/10130f2de9b5763c1aef2f1ed20a2deed8b09274

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. J. Alicea
2. N. Lindner
3. A. Stern
4. C. Nayak
5. P. Fendley
6. L. Balents
7. Erez Berg
8. Roger S. K. Mong

In Condensed Matter Physics

1. J. Alicea
2. L. Balents
3. Zhenghan Wang
4. Erez Berg
5. Roger S. K. Mong
6. M. Hermanns
7. A. Stern
8. C. Nayak

In Nuclear and High Energy Physics

1. Matthew Fisher
2. Erez Berg

Citations in the corpus

• Fractional quantum Hall physics in topological flat bands (2013, unknown): “Note that in a periodic system with topological order there is some ambiguity as to the treatment of degenerate eigenstates; Bernevig and Regnault chose to study a uniform incoherent superposition of the q degenerate Laughlin states, but the phase dependence of the entanglement entropy of coherent s”
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure (2013, background): “(They are also referred to as ‘minimum entangled states’ [137].)”
• Quantum Hall physics : Hierarchies and conformal field theory techniques (2016, background): “…Levin and Wen (2006), is currently the most commonly used entanglement measure.22 It contains, in principle, all the information about the S-matrix, and thus the quasiparticle excitations (Zhang et al., 2012), and gives direct access to the total quantum dimension of the underlying field theory.”
• Identifying topological order by entanglement entropy (2012, methodology): “Moreover, in general the universal value is achieved for so-called Minimal Entropy States (MES’s) (10), which correspond to states in which a quasiparticle is definitely contained within the region A (or B).”