Vortex patterns in the almost-bosonic anyon gas

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. PACS numbers: 05.30.Pr, 03.75.HhThe eventual unambiguous observation of the elusive exotic particles going under the name of anyons [19,26,28,40] remains one the most exciting prospects of condensed matter physics. Apart from speculative applications [27], much excitement comes from the possibility of observing quasi-particles [3,16,17] who do not fall into the ubiquitous dichotomy between bosons and fermions.

Synthetic flux attachment

“…Only recently have we become aware of the work in Refs. [160,161], for which a similar effective theory is considered. We find consistent findings with these studies at the points where both works overlap.…”

Semiclassical Limit for Almost Fermionic Anyons

“…They have been conjectured [2,42,53] to be relevant for the fractional quantum Hall effect (see [24,30,28] for review). They could also be simulated in certain cold atoms systems with synthetic gauge fields [17,10,61,63,64,12].…”

Quantum impurity model for anyons

“…[66][67][68][69][70][71]. Another approach has been to first regularize the Hamiltonian (5) by making the fluxes extended [72][73][74][75], and in this situation an exact averagefield theory and a corresponding Thomas-Fermi theory may be derived in the almost-bosonic limit α ∼ N −1 → 0 [28,[76][77][78][79]. Also singular or point-interacting anyons may be considered [80][81][82][83][84], as well as anyons regularized by a strong magnetic field [85].…”

“…From the practical point of view, however, it does not give much insight concerning a physical realization. Indeed there has been a recent upsurge in interest concerning the realization of anyons as emergent quasiparticles in experimentally feasible systems, in particular from the perspective of deriving robust, testable predictions such as density signatures [22][23][24][25][26][27][28]. Also the emergence of anyons in a FQHE setting by means of attachment of flux via Laughlin quasiholes was recently revisited and elaborated on arXiv:1912.07890v1 [cond-mat.quant-gas] 17 Dec 2019 in Ref.…”