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This study establishes that the Hofstadter butterfly's topological features persist in interacting fermion systems, providing a rigorous link between theoretical quantum maps and measurable Hall conductivity without relying on perturbative approximations. By confirming quantized conductance values even with electron interactions, this non-perturbative framework advances our ability to model many-body phases essential for robust metrology and future quantum computing architectures.

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Hokkaido University Team Models Many-Body Quantum Hall Phase Diagram for Fermion Systems

Quantum ZeitgeistJuly 16, 20266 min read

The celebrated Hofstadter butterfly diagram, long a theoretical ideal, now directly links to measurable electrical currents in real materials. Previously, understanding how electron interactions altered this map of quantum behaviour remained a challenge, but this work establishes a clear connection between the butterfly’s ‘colours’ and the proportionality constant in Ohm’s law. This allows prediction of Hall conductivity even when electrons interact, opening new avenues for designing advanced electronic devices.

Giovanna Marcelli from Roma Tre University and colleagues at Hokkaido University, Sapienza University of Rome, and the University of Tübingen reveal that the familiar coloured Hofstadter butterfly holds a key interpretation for interacting quantum systems. The team identifies locally unique gapped ground states within a parameter space defined by magnetic field, chemical potential, and interaction strength. Their findings rigorously show that the integer 'colours' of the non-interacting butterfly continue to represent quantized Hall conductivity in these interacting systems, offering a new understanding of many-body quantum Hall phases and extending this understanding to both commensurate and incommensurate magnetic fluxes. Quantised Hall conductivity directly links to Hofstadter butterfly features…

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