For a 2D Fermi liquid, the de Haas-van Alphen amplitudes are derived from the zero-mode sector of a coadjoint-orbit bosonized action, yielding LK-like low-T behavior and a second harmonic A2 that changes sign at high T.
The origin of holomorphic states in Landau levels from non-commutative geometry, and a new formula for their overlaps on the torus
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abstract
Holomorphic functions that characterize states in a two-dimensional Landau level been central to key developments such as the Laughlin state. Their origin has historically been attributed to a special property of "Schr\"odinger wavefunctions" of states in the "lowest Landau level". It is shown here that they instead arise in any Landau level as a generic mathematical property of the Heisenberg description of the non-commutative geometry of guiding centers. When quasiperiodic boundary conditions are applied to compactify the system on a torus, a new formula for the overlap between holomorphic states, in the form of a discrete sum rather than an integral, is obtained. The new formula is unexpected from the previous "lowest-Landau level Schr\"odinger wavefunction" interpretation.
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Bosonized theory of de Haas-van Alphen quantum oscillation in Fermi liquids
For a 2D Fermi liquid, the de Haas-van Alphen amplitudes are derived from the zero-mode sector of a coadjoint-orbit bosonized action, yielding LK-like low-T behavior and a second harmonic A2 that changes sign at high T.