Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1901.10739 · Europhysics Letters (EPL)

Vortex patterns in the almost-bosonic anyon gas

Michele Correggi, Romain Duboscq, Douglas Lundholm, Nicolas Rougerie

Published Jun 7, 2019• 22 citations
arXivHTMLPDF

Abstract

We study theoretically and numerically the ground state of a gas of 2D Abelian anyons in an external trapping potential. We treat anyon statistics in the magnetic gauge picture, perturbatively around the bosonic end. This leads to a mean-field energy functional, whose ground state displays vortex lattices similar to those found in rotating Bose-Einstein condensates. A crucial difference is, however, that the vortex density is proportional to the underlying matter density of the gas.

DOI
10.1209/0295-5075/126/20005

Related papers

Vortex patterns in the almost-bosonic anyon gas

Michele Correggi, Romain Duboscq, Douglas Lundholm +1 more

We study theoretically and numerically the ground state of a gas of 2D abelian anyons in an external trapping potential.We treat anyon statistics in the magnetic gauge picture, perturbatively around the bosonic end.This leads to a mean-field energy functional, whose ground state displays vortex lattices similar to those found in rotating Bose-Einstein condensates.A crucial difference is however that the vortex density is proportional to the underlying matter density of the gas.

•Jan 29, 2019•10 citations

Vortex lattices in Bose-Einstein condensates: From the Thomas-Fermi regime to the lowest-Landau-level regime

Marco Cozzini, S. Stringari, C. Tozzo

We consider a periodic vortex lattice in a rotating Bose-Einstein-condensed gas, where the centrifugal potential is exactly compensated by the external harmonic trap. By introducing a gauge transformation which makes the Hamiltonian periodic, we numerically solve the two-dimensional (2D) Gross-Pitaevskii equation finding the exact mean field ground state. In particular, we explore the crossover between the Thomas-Fermi regime, holding for large values of the coupling constant, and the lowest Landau level limit, corresponding to the weakly interacting case. Explicit results are given for the equation of state, the vortex core size, as well as the elastic shear modulus, which is crucial for the calculation of the Tkachenko frequencies.

arXiv:cond-mat/0509559•Physical Review A•Feb 22, 2006•19 citations

Magnetic Thomas-Fermi theory for 2D abelian anyons

Antoine Levitt, Douglas Lundholm, Nicolas Rougerie

Two-dimensional abelian anyons are, in the magnetic gauge picture, represented as fermions coupled to magnetic flux tubes. For the ground state of such a system in a trapping potential, we theoretically and numerically investigate a Hartree approximate model, obtained by restricting trial states to Slater determinants and introducing a self-consistent magnetic field, locally proportional to matter density. This leads to a fermionic variant of the Chern-Simons-Schrödinger system. We find that for dense systems, a semi-classical approximation yields qualitatively good results. Namely, we derive a density functional theory of magnetic Thomas-Fermi type, which correctly captures the trends of our numerical results. In particular, we explore the subtle dependence of the ground state with respect to the fraction of magnetic flux units attached to particles.

arXiv:2504.13481•SciPost Physics Core•Mar 30, 2026•1 citation

Average field approximation for almost bosonic anyons in a magnetic field

Théotime Girardot

We study the ground state of a large number N of 2D extended anyons in an external magnetic field. We consider a scaling limit where the statistics parameter α is proportional to N−1 when N → ∞, which allows the statistics to be seen as a “perturbation around the bosonic end.” Our model is that of bosons in a magnetic field interacting through long-range magnetic potential generated by magnetic charges carried by each particle, smeared over discs of radius R. Our method allows us to take R → 0 not too fast at the same time as N → ∞ : R = N−1/4+ɛ. We use the information theoretic version of the de Finetti theorem of Brandão and Harrow to justify the so-called “average field approximation”: the particles behave like independent, identically distributed bosons interacting via a self-consistent magnetic field.

arXiv:1910.09310•Journal of Mathematical Physics•Jul 1, 2020•15 citations

Vortex patterns of atomic Bose-Einstein condensates in a density-dependent gauge potential

Matthew Edmonds, Muneto Nitta

We theoretically examine the vortex states of a gas of trapped quasi-two-dimensional ultracold bosons subject to a density-dependent gauge potential, realizing an effective nonlinear rotation of the atomic condensate, which we also show is within the reach of current experimental techniques with ultracold atom experiments. The nonlinear rotation has a twofold effect; as well as distorting the shape of the condensate it also leads to an inhomogeneous vorticity resulting in unique morphological and topological states, including ring vortex arrangements that do not follow the standard Abrikosov result. The dynamics of trapped vortices are also explored, which differ from the case of rigid-body rotation due to the absence of a global laboratory reference frame.

arXiv:2002.09189•Physical Review A•Jul 27, 2020•18 citations

Vortex lattices for ultracold bosonic atoms in a non-Abelian gauge potential

Stavros Komineas, Nigel R. Cooper

The use of coherent optical dressing of atomic levels allows the coupling of ultracold atoms to effective nondynamical gauge fields. These can be used to generate effective magnetic fields and have the potential to generate non-Abelian gauge fields. We consider a model of a gas of bosonic atoms coupled to a gauge field with $\text{U}(2)$ symmetry and with constant effective magnetic field. We include the effects of weak contact interactions by applying Gross-Pitaevskii mean-field theory. We study the effects of a $\text{U}(2)$ non-Abelian gauge field on the vortex lattice phase induced by a uniform effective magnetic field, generated by an Abelian gauge field or, equivalently, by rotation of the gas. We show that, with increasing non-Abelian gauge field, the nature of the ground state changes dramatically, with structural changes of the vortex lattice. We show that the effect of the non-Abelian gauge field is equivalent to the introduction of effective interactions with nonzero range. We also comment on the consequences of the non-Abelian gauge field for strongly correlated fractional quantum Hall states.

arXiv:1203.3308•Physical Review A•May 16, 2012•11 citations
We study theoretically and numerically the ground state of a gas of 2D Abelian anyons in an external trapping potential. We treat anyon statistics in the magnetic gauge picture, perturbatively around the bosonic end. This leads to a mean-field energy functional, whose ground state displays vortex lattices similar to those found in rotating Bose-Einstein condensates. A crucial difference is, however, that the vortex density is proportional to the underlying matter density of the gas.
We consider a periodic vortex lattice in a rotating Bose-Einstein-condensed gas, where the centrifugal potential is exactly compensated by the external harmonic trap. By introducing a gauge transformation which makes the Hamiltonian periodic, we numerically solve the two-dimensional (2D) Gross-Pitaevskii equation finding the exact mean field ground state. In particular, we explore the crossover between the Thomas-Fermi regime, holding for large values of the coupling constant, and the lowest Landau level limit, corresponding to the weakly interacting case. Explicit results are given for the equation of state, the vortex core size, as well as the elastic shear modulus, which is crucial for the calculation of the Tkachenko frequencies.
Two-dimensional abelian anyons are, in the magnetic gauge picture, represented as fermions coupled to magnetic flux tubes. For the ground state of such a system in a trapping potential, we theoretically and numerically investigate a Hartree approximate model, obtained by restricting trial states to Slater determinants and introducing a self-consistent magnetic field, locally proportional to matter density. This leads to a fermionic variant of the Chern-Simons-Schrödinger system. We find that for dense systems, a semi-classical approximation yields qualitatively good results. Namely, we derive a density functional theory of magnetic Thomas-Fermi type, which correctly captures the trends of our numerical results. In particular, we explore the subtle dependence of the ground state with respect to the fraction of magnetic flux units attached to particles.
We study the ground state of a large number N of 2D extended anyons in an external magnetic field. We consider a scaling limit where the statistics parameter α is proportional to N−1 when N → ∞, which allows the statistics to be seen as a “perturbation around the bosonic end.” Our model is that of bosons in a magnetic field interacting through long-range magnetic potential generated by magnetic charges carried by each particle, smeared over discs of radius R. Our method allows us to take R → 0 not too fast at the same time as N → ∞ : R = N−1/4+ɛ. We use the information theoretic version of the de Finetti theorem of Brandão and Harrow to justify the so-called “average field approximation”: the particles behave like independent, identically distributed bosons interacting via a self-consistent magnetic field.
We theoretically examine the vortex states of a gas of trapped quasi-two-dimensional ultracold bosons subject to a density-dependent gauge potential, realizing an effective nonlinear rotation of the atomic condensate, which we also show is within the reach of current experimental techniques with ultracold atom experiments. The nonlinear rotation has a twofold effect; as well as distorting the shape of the condensate it also leads to an inhomogeneous vorticity resulting in unique morphological and topological states, including ring vortex arrangements that do not follow the standard Abrikosov result. The dynamics of trapped vortices are also explored, which differ from the case of rigid-body rotation due to the absence of a global laboratory reference frame.
The use of coherent optical dressing of atomic levels allows the coupling of ultracold atoms to effective nondynamical gauge fields. These can be used to generate effective magnetic fields and have the potential to generate non-Abelian gauge fields. We consider a model of a gas of bosonic atoms coupled to a gauge field with U(2)\text{U}(2)U(2) symmetry and with constant effective magnetic field. We include the effects of weak contact interactions by applying Gross-Pitaevskii mean-field theory. We study the effects of a U(2)\text{U}(2)U(2) non-Abelian gauge field on the vortex lattice phase induced by a uniform effective magnetic field, generated by an Abelian gauge field or, equivalently, by rotation of the gas. We show that, with increasing non-Abelian gauge field, the nature of the ground state changes dramatically, with structural changes of the vortex lattice. We show that the effect of the non-Abelian gauge field is equivalent to the introduction of effective interactions with nonzero range. We also comment on the consequences of the non-Abelian gauge field for strongly correlated fractional quantum Hall states.