Scale Invariance in the Lowest Landau Level
نویسندگان
چکیده
We show that the discrete set of pair amplitudes $A_m$ introduced by Haldane are an angular-momentum resolved generalization Tan two-body contact, which parametrizes universal short-range correlations in atomic quantum gases. The provide a complete description translation-invariant and rotation-invariant states lowest Landau level (LLL), both compressible incompressible. To leading nontrivial order beyond non-interacting high-temperature limit, they determined analytically terms pseudopotential parameters $V_m$, provides qualitative crossover towards incompressible ground for different filling factors. Moreover, we contact interactions $\sim g_2 \delta^{(2)}({\bf x})$, scale invariant at classical level, non-commutativity guiding center coordinates gives rise to anomaly commutator $i [\hat{H}_{\rm LLL}, \hat{D}_R] = (2 + \ell \partial_\ell) \hat{H}_{\rm LLL}$ with dilatation operator $\hat{D}_R$ LLL, replaces trace absence magnetic field. interaction-induced breaking invariance finite frequency shift breathing mode harmonic trap, describes transitions between levels, strength is estimated relevant dimensionless coupling constant $\tilde{g}_2$.
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ژورنال
عنوان ژورنال: Comptes Rendus Physique
سال: 2023
ISSN: ['1878-1535', '1631-0705']
DOI: https://doi.org/10.5802/crphys.137