2024/12/30 by Ben Currie, Currie, Ben, Evgeny Kozik +1
Computer Science · Engineering · Physics and Astronomy · #FOS: Physical sciences #Low-power high-performance VLSI design #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Information and Cryptography #Quantum and electron transport phenomena #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2412.21064
openalex publication_date 2024/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The fractional quantum Hall (FQH) effect arises from strong electron correlations in a quantising magnetic field, and features exotic emergent phenomena such as electron fractionalisation. Using the diagrammatic Monte Carlo approach with the combinatorial summation (CoS) algorithm, we obtain results with controlled accuracy for the microscopic model of interacting electrons in the lowest Landau level (LLL) in the thermodynamic limit. Starting from the macroscopically degenerate LLL at finite temperature, including interactions order by order, and applying a controlled resummation to the resulting series, we observe the emergence of the incompressible 1/3-filled state as the temperature is lowered. By analysing the long-time decay of the Green's function, we find spectral properties consistent with an energy gap at 1/3-filling, whereas at 1/2-filling our results are consistent with the pseudogapped behaviour previously observed experimentally and suggested theoretically. 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, while also showing applicability of expansions in the bare Coulomb potential for precision calculations.