期刊
PHYSICAL REVIEW X
卷 5, 期 2, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevX.5.021004
关键词
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资金
- DARPA QuEST program
- AFOSR [FA9550-10-1-0524, FA9550-11-1-0313]
- Office of Research and Sponsored Programs at California State University Long Beach
- Swiss National Science Foundation through the National Competence Center in Research QSIT
- European Research Council
- NSF [1066293]
- Swiss National Supercomputing Centre (CSCS) [s395]
Interesting non-Abelian states, e.g., the Moore-Read Pfaffian and the anti-Pfaffian, offer candidate descriptions of the nu = 5/2 fractional quantum Hall state. But, the significant controversy surrounding the nature of the nu = 5/2 state has been hampered by the fact that the competition between these and other states is affected by small parameter changes. To study the phase diagram of the nu = 5/2 state, we numerically diagonalize a comprehensive effective Hamiltonian describing the fractional quantum Hall effect of electrons under realistic conditions in GaAs semiconductors. The effective Hamiltonian takes Landau-level mixing into account to lowest order perturbatively in kappa, the ratio of the Coulomb energy scale to the cyclotron gap. We also incorporate the nonzero width w of the quantum-well and subband mixing. We find the ground state in both the torus and spherical geometries as a function of kappa and w. To sort out the nontrivial competition between candidate ground states, we analyze the following four criteria: its overlap with trial wave functions, the magnitude of energy gaps, the sign of the expectation value of an order parameter for particle-hole symmetry breaking, and the entanglement spectrum. We conclude that the ground state is in the universality class of the Moore-Read Pfaffian state, rather than the anti-Pfaffian, for kappa < kappa(c)(w), where kappa(c)(w) is a w-dependent critical value 0.6 less than or similar to kappa(c) (w) less than or similar to 1. We observe that both Landau-level mixing and nonzero width suppress the excitation gap, but Landau-level mixing has a larger effect in this regard. Our findings have important implications for the identification of non-Abelian fractional quantum Hall states.
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