Microscopic derivation of the stationary Chern-Simons-Schrödinger equation for almost-bosonic anyons
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2025
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| _version_ | 1866913806754512896 |
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| author | Ataei, Alireza Lundholm, Douglas Girardot, Théotime |
| author_facet | Ataei, Alireza Lundholm, Douglas Girardot, Théotime |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_17488 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Microscopic derivation of the stationary Chern-Simons-Schrödinger equation for almost-bosonic anyons Ataei, Alireza Lundholm, Douglas Girardot, Théotime Mathematical Physics Quantum Gases Strongly Correlated Electrons Analysis of PDEs Quantum Physics 81V27, 81V70, 35Q55, 47J30 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. |
| title | Microscopic derivation of the stationary Chern-Simons-Schrödinger equation for almost-bosonic anyons |
| topic | Mathematical Physics Quantum Gases Strongly Correlated Electrons Analysis of PDEs Quantum Physics 81V27, 81V70, 35Q55, 47J30 |
| url | https://arxiv.org/abs/2504.17488 |