Vortex lattice solutions of the ZHK Chern–Simons equations

Rajaratnam, Krishan; Sigal, Israel Michael

doi:10.1088/1361-6544/ab9248

Nonlinearity

2020

DOI: 10.1088/1361-6544/ab9248

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Vortex lattice solutions of the ZHK Chern–Simons equations

Krishan Rajaratnam

Israel Michael Sigal

Abstract: We consider the non-relativistic Chern-Simons equations proposed by Zhang, Hansen and Kivelson as the mean eld theory of the fractional Hall effect. We prove the existence of the vortex lattice solutions (i.e. solution with lattice symmetry and with topological degree one per lattice cell) similar to the Abrikosov solutions of superconductivity. We derive an asymptotic expression for the energy per unit area and show that it attains minimum at the hexagonal lattice.

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2024

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“…However, we expect the qualitative findings to be general. Note the kinship of this formalism with that of Chern-Simons theory, see [30][31][32] and references therein. In [33][34][35] it is also proposed that density-dependent synthetic gauge fields can be created by submitting a Bose gas to both rotation and laser-matter coupling.…”

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confidence: 99%

Vortex patterns in the almost-bosonic anyon gas

Correggi¹,

Duboscq²,

Lundholm³

et al. 2019

EPL

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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.

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confidence: 99%

Vortex patterns in the almost-bosonic anyon gas

Correggi¹,

Duboscq²,

Lundholm³

et al. 2019

EPL

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Instability of Electroweak Homogeneous Vacua in Strong Magnetic Fields

Gardner,

Sigal

2024

Ann. Henri Poincaré

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We consider the classical vacua of the Weinberg–Salam (WS) model of electroweak forces. These are no-particle, static solutions to the WS equations minimizing the WS energy locally. We study the WS vacuum solutions exhibiting a non-vanishing average magnetic field of strength b and prove that (i) there is a magnetic field threshold $$b_*$$ b ∗ such that for $$b<b_*$$ b < b ∗ , the vacua are translationally invariant (and the magnetic field is constant), while, for $$b>b_*$$ b > b ∗ , they are not, (ii) for $$b>b_*$$ b > b ∗ , there are non-translationally invariant solutions with lower energy per unit volume and with the discrete translational symmetry of a 2D lattice in the plane transversal to b, and (iii) the lattice minimizing the energy per unit volume approaches the hexagonal one as the magnetic field strength approaches the threshold $$b_*$$ b ∗ . In the absence of particles, the Weinberg–Salam model reduces to the Yang–Mills–Higgs (YMH) equations for the gauge group U(2). Thus, our results can be rephrased as the corresponding statements about the U(2)-YMH equations.

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Vortex lattice solutions of the ZHK Chern–Simons equations

Cited by 2 publications

References 34 publications

Vortex patterns in the almost-bosonic anyon gas

Vortex patterns in the almost-bosonic anyon gas

Instability of Electroweak Homogeneous Vacua in Strong Magnetic Fields

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