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arXiv:2504.17488

Microscopic derivation of the stationary Chern-Simons-Schrödinger equation for almost-bosonic anyons

Alireza Ataei, Douglas Lundholm, Théotime Girardot

Published Apr 24, 2025• 0 citations
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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 $2πβ$ to remain finite, we rigorously derive the stationary Chern-Simons-Schrödinger/average-field-Pauli effective energy density functional for the condensate wave function. This includes a scalar self-interaction parameter $γ$ which depends both on $β$, 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 $γ=2π|β|$. Our findings confirm and clarify the predictions we have found in the physics literature.

DOI
10.48550/arxiv.2504.17488

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