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

• URL: http://arxiv.org/abs/2305.09286v3
• Date: Tue, 15 Aug 2023 01:50:51 GMT
• Title: From frustration-free parent Hamiltonians to off-diagonal long-range order: Moore-Read and related states in second quantization
• Authors: Fanmao Zhang, Matheus Schossler, Alexander Seidel, Li Chen
• Abstract summary: We construct a second-quantized formula for Moore-Read Pfaffian states. We prove the existence of frustration-free parent Hamiltonians without appealing to such second-quantized properties.
• Score: 51.47980393607887
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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