Microscopic derivation of the stationary Chern-Simons-Schrödinger equation for almost-bosonic anyons
- URL: http://arxiv.org/abs/2504.17488v1
- Date: Thu, 24 Apr 2025 12:29:20 GMT
- Title: Microscopic derivation of the stationary Chern-Simons-Schrödinger equation for almost-bosonic anyons
- Authors: Alireza Ataei, Douglas Lundholm, Théotime Girardot,
- Abstract summary: This work considers the microscopic structure of a quantum gas of almost-bosonic anyons.<n>We rigorously derive the stationary Chern-Simons-Schr"odinger/average-field-Pauli effective energy density functional for the condensate wave function.<n>Our findings confirm and clarify the predictions we have found in the physics literature.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this work we consider the $N$-body Hamiltonian describing the microscopic structure of a quantum gas of almost-bosonic anyons. This description includes both extended magnetic flux and spin-orbit/soft-disk interaction between the particles which are confined in a scalar trapping potential. We study a physically well-motivated ansatz for a sequence of trial states, consisting of Jastrow repulsive short-range correlations and a condensate, with sufficient variational freedom to approximate the ground state (and possibly also low-energy excited states) of the gas. In the limit $N \to \infty$, while taking the relative size of the anyons to zero and the total magnetic flux $2\pi\beta$ to remain finite, we rigorously derive the stationary Chern-Simons-Schr\"odinger/average-field-Pauli effective energy density functional for the condensate wave function. This includes a scalar self-interaction parameter $\gamma$ which depends both on $\beta$, the diluteness of the gas, and the spin-orbit coupling strength $g$, but becomes independent of these microscopic details for a particular value of the coupling $g=2$ in which supersymmetry is exhibited (on all scales, both microscopic and mesoscopic) with $\gamma=2\pi|\beta|$. Our findings confirm and clarify the predictions we have found in the physics literature.
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