From frustration-free parent Hamiltonians to off-diagonal long-range order: Moore-Read and related states in second quantization

Abstract

We construct a recursive second-quantized formula for Moore-Read Pfaffian states. We demonstrate the utility of such second-quantized presentations by directly proving the existence of frustration-free parent Hamiltonians, without appealing to polynomial clustering properties. Furthermore, we show how this formalism is connected to the existence of a non-local order parameter for Moore-Read states and give a proof that the latter exhibit off-diagonal long-range order (ODLRO) in these quantities. We also develop a similar second-quantized presentation for the fermionic antiand PH-Pfaffian states, as well as f- and higher wave paired composite fermion states, and discuss ODLRO in most cases.

arXiv commentTwo references have been updated

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Cited by in corpus (4)

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• Fusion mechanism for quasiparticles and topological quantum order in the lowest Landau level
• Linking infinite bond-dimension matrix product states with frustration-free Hamiltonians
• Second-quantized approach to the study of Halperin state in fractional quantum Hall effect