Fractional quantum Hall effect from frustration-free Hamiltonians

• 主要作者: Yang, Bo
• 其他作者: School of Physical and Mathematical Sciences
• 格式: Article
• 語言: English
• 出版: 2020
• 主題: Science::Physics; Hall Effect; Hamiltonians
• 在線閱讀: https://hdl.handle.net/10356/145072
• 機構: Nanyang Technological University

We show that there is an emergent lattice description for the continuous fractional quantum Hall (FQH) systems, with a generalized set of few-body coherent states. In particular, model Hamiltonians of the FQH effect (FQHE) are equivalent to the real-space von Neumann lattice of local projection operators imposed on a continuous system in the thermodynamic limit. It can be analytically derived that tuning local one-body potentials in such lattices amounts to the tuning of individual two- or few-body pseudopotentials. For some cases, we can realize pure few-body pseudopotentials important for stabilizing exotic non-Abelian topological phases. Thus, this new approach can potentially lead to the experimental realization of coveted non-Abelian quantum fluids including the Moore-Read state and the Fibonacci state. The reformulation of the FQHE as a sum of local projections opens up new paths for rigorously proving the incompressibility of microscopic Hamiltonians in the thermodynamic limit.