Fractional quantum Hall effect from frustration-free Hamiltonians

Abstract

We show that there is an emergent lattice description for the continuous fractional quantum Hall (FQH) systems, with a generalised set of few-body coherent states. In particular, model Hamiltonians of the FQH effect 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 realise pure few-body pseudopotentials important for stabilising exotic non-Abelian topological phases. This new approach can thus potentially lead to experimental realisation 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 path for rigorously proving the incompressibility of microscopic Hamiltonians in the thermodynamic limit.

4+ pages, supplementary materials attached, comments very welcome

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Cited by in corpus (5)

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• Analytic exposition of the graviton modes in fractional quantum Hall effects and its physical implications
• Fractionalisation and dynamics of anyons at $\nu =n+1/3$ in fractional quantum Hall effect and their experimental signatures
• Models of interacting bosons with exact ground states: a unified approach
• Superlattice induced electron percolation within a single Landau level