TY - JOUR

T1 - Fractional Quantum Hall States at ν=13/5 and 12/5 and Their Non-Abelian Nature

AU - Zhu, W.

AU - Gong, S. S.

AU - Haldane, F. D.M.

AU - Sheng, D. N.

N1 - Publisher Copyright:
© 2015 American Physical Society.

PY - 2015/9/18

Y1 - 2015/9/18

N2 - Topological quantum states with non-Abelian Fibonacci anyonic excitations are widely sought after for the exotic fundamental physics they would exhibit, and for universal quantum computing applications. The fractional quantum Hall (FQH) state at a filling factor of ν=12/5 is a promising candidate; however, its precise nature is still under debate and no consensus has been achieved so far. Here, we investigate the nature of the FQH ν=13/5 state and its particle-hole conjugate state at 12/5 with the Coulomb interaction, and we address the issue of possible competing states. Based on a large-scale density-matrix renormalization group calculation in spherical geometry, we present evidence that the essential physics of the Coulomb ground state (GS) at ν=13/5 and 12/5 is captured by the k=3 parafermion Read-Rezayi state (RR3), including a robust excitation gap and the topological fingerprint from the entanglement spectrum and topological entanglement entropy. Furthermore, by considering the infinite-cylinder geometry (topologically equivalent to torus geometry), we expose the non-Abelian GS sector corresponding to a Fibonacci anyonic quasiparticle, which serves as a signature of the RR3 state at 13/5 and 12/5 filling numbers.

AB - Topological quantum states with non-Abelian Fibonacci anyonic excitations are widely sought after for the exotic fundamental physics they would exhibit, and for universal quantum computing applications. The fractional quantum Hall (FQH) state at a filling factor of ν=12/5 is a promising candidate; however, its precise nature is still under debate and no consensus has been achieved so far. Here, we investigate the nature of the FQH ν=13/5 state and its particle-hole conjugate state at 12/5 with the Coulomb interaction, and we address the issue of possible competing states. Based on a large-scale density-matrix renormalization group calculation in spherical geometry, we present evidence that the essential physics of the Coulomb ground state (GS) at ν=13/5 and 12/5 is captured by the k=3 parafermion Read-Rezayi state (RR3), including a robust excitation gap and the topological fingerprint from the entanglement spectrum and topological entanglement entropy. Furthermore, by considering the infinite-cylinder geometry (topologically equivalent to torus geometry), we expose the non-Abelian GS sector corresponding to a Fibonacci anyonic quasiparticle, which serves as a signature of the RR3 state at 13/5 and 12/5 filling numbers.

UR - http://www.scopus.com/inward/record.url?scp=84942154815&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84942154815&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.115.126805

DO - 10.1103/PhysRevLett.115.126805

M3 - Article

C2 - 26431006

AN - SCOPUS:84942154815

VL - 115

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 12

M1 - 126805

ER -