Strange Metal to Insulator Transitions in the Lowest Landau Level

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Abstract

We study the microscopic model of electrons in the partially-filled lowest Landau level interacting via the Coulomb potential by the diagrammatic theory within the GW approximation. In a wide range of filling fractions and temperatures, we find a homogeneous non-Fermi liquid (nFL) state similar to that found in the Sachdev-Ye-Kitaev (SYK) model, with logarithmic corrections to the anomalous dimension. In addition, the phase diagram is qualitatively similar to that of SYK: a first-order transition terminating at a critical end-point separates the nFL phase from a band insulator that corresponds to the fully filled Landau level. This critical point, as well as that of the SYK model - whose critical exponents we determine more precisely - are shown to both belong to the Van der Waals universality class. The possibility of a charge density wave (CDW) instability is also investigated, and we find the homogeneous nFL state to extend down to the ground state for fillings 0.2≲ν ≲0.8, while a CDW appears outside this range of fillings at sufficiently low temperatures. Our results suggest that the SYK-like nFL state should be a generic feature of the partially filled lowest Landau level at intermediate temperatures.

Original languageEnglish
Article number023210
JournalPhysical Review Research
Volume6
Issue number2
DOIs
Publication statusPublished - 24 May 2024

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