Controlled description of fractional quantum Hall physics by Feynman's diagrammatic expansion.

The fractional quantum Hall (FQH) effect is an archetypal model of strong electronic correlations, featuring exotic emergent phenomena such as electron fractionalisation. Using the diagrammatic Monte Carlo approach with the combinatorial summation algorithm, we obtain results with controlled accuracy for the microscopic model of interacting electrons in the lowest Landau level. As the temperature is lowered, we study the development and emergence of the incompressible 1/3-filled FQH state. Our work provides the first demonstration that fractionalised phases of matter can be reliably described with Feynman's diagrammatic technique in terms of the fundamental electronic degrees of freedom.