Fractional quantum Hall effect from frustration-free Hamiltonians

TL;DR

This paper introduces an emergent lattice framework for the fractional quantum Hall effect, linking continuous systems to lattice models with local projections, enabling new insights into topological phases and potential experimental realizations.

Contribution

It establishes a lattice description for FQH systems using local projection operators, connecting continuous models to lattice Hamiltonians and facilitating the study of non-Abelian topological phases.

Findings

Lattice description equivalent to continuous FQH systems in the thermodynamic limit.

Tuning local potentials corresponds to adjusting pseudopotentials.

Potential realization of non-Abelian phases like Moore-Read and Fibonacci states.

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.