The boundary density profile of a Coulomb droplet. Freezing at the edge

Cardoso, Gabriel; Stéphan, Jean-Marie; Abanov, Alexander G.

doi:10.1088/1751-8121/abcab9

Cited by 15 publications

(20 citation statements)

References 55 publications

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“…Further analysis of the N = 200 data of ref. [51] confirms the values (4.3). The results of the fit are shown in figure 4.…”

Section: Jhep05(2021)120supporting

confidence: 85%

“…As explained in ref. [51], these fluctuations near the boundary correspond to the preemptive freezing of Hall electrons into a Wigner crystal, starting from the outer parts of the droplet.…”

Section: Jhep05(2021)120mentioning

confidence: 97%

“…• The prediction for the density profile (3.33) can be compared with the numerical results of ref. [51] by considering densities of nearby electron numbers. The analytic studies of the density profile in ref.…”

Section: Jhep05(2021)120mentioning

confidence: 99%

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W-infinity symmetry in the quantum hall effect beyond the edge

Cappelli

Maffi

2021

J. High Energ. Phys.

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The description of chiral quantum incompressible fluids by the W∞ symmetry can be extended from the edge, where it encompasses the conformal field theory approach, to the non-conformal bulk. The two regimes are characterized by excitations with different sizes, energies and momenta within the disk geometry. In particular, the bulk quantities have a finite limit for large droplets. We obtain analytic results for the radial shape of excitations, the edge reconstruction phenomenon and the energy spectrum of density fluctuations in Laughlin states.

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“…Further analysis of the N = 200 data of ref. [51] confirms the values (4.3). The results of the fit are shown in figure 4.…”

Section: Jhep05(2021)120supporting

confidence: 85%

Section: Jhep05(2021)120mentioning

confidence: 97%

See 1 more Smart Citation

W-infinity symmetry in the quantum hall effect beyond the edge

Cappelli

Maffi

2021

J. High Energ. Phys.

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“…It makes the asymptotic analysis of the kernel in various scaling limits possible, as will be the main topic of this work. The situation is much more difficult for Coulomb gases at general values of β ̸ = 2, see [9,24,47] and references therein for recent developments.…”

Section: Introductionmentioning

confidence: 99%

Scaling Limits of Planar Symplectic Ensembles

Akemann¹,

Byun²,

Kang³

2022

SIGMA

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We consider various asymptotic scaling limits N → ∞ for the 2N complex eigenvalues of non-Hermitian random matrices in the symmetry class of the symplectic Ginibre ensemble. These are known to be integrable, forming Pfaffian point processes, and we obtain limiting expressions for the corresponding kernel for different potentials. The first part is devoted to the symplectic Ginibre ensemble with the Gaussian potential. We obtain the asymptotic at the edge of the spectrum in the vicinity of the real line. The unifying form of the kernel allows us to make contact with the bulk scaling along the real line and with the edge scaling away from the real line, where we recover the known determinantal process of the complex Ginibre ensemble. Part two covers ensembles of Mittag-Leffler type with a singularity at the origin. For potentials Q(ζ) = |ζ| 2λ − (2c/N ) log |ζ|, with λ > 0 and c > −1, the limiting kernel obeys a linear differential equation of fractional order 1/λ at the origin. For integer m = 1/λ it can be solved in terms of Mittag-Leffler functions. In the last part, we derive Ward's equation for planar symplectic ensembles for a general class of potentials. It serves as a tool to investigate the Gaussian and singular Mittag-Leffler universality class. This allows us to determine the functional form of all possible limiting kernels (if they exist) that are translation invariant, up to their integration domain.

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“…It makes the asymptotic analysis of the kernel in various scaling limits possible, as will be the main topic of this work. The situation is much more difficult for Coulomb gases at general values of β = 2, see [7,18,39] and references therein for recent developments.…”

Section: Introductionmentioning

confidence: 99%

Scaling Limits of Planar Symplectic Ensembles

Akemann,

Byun,

Kang

2021

Preprint

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We consider various asymptotic scaling limits N → ∞ for the 2N complex eigenvalues of non-Hermitian random matrices in the symmetry class of the symplectic Ginibre ensemble. These are known to be integrable, forming Pfaffian point processes, and we obtain limiting expressions for the corresponding kernel for different potentials. The first part is devoted to the symplectic Ginibre ensemble with a Gaussian potential. We obtain the asymptotic at the edge of the spectrum in the vicinity of the real line. The unifying form of the kernel allows us to make contact with the bulk scaling along the real line and with the edge scaling away from the real line, where we recover the known determinantal process of the complex Ginibre ensemble. Part two covers ensembles of Mittag-Leffler type with a singularity at the origin. For potentials Q(ζ) = |ζ| 2λ − (2c/N ) log |ζ|, with λ > 0 and c > −1, the limiting kernel obeys a linear differential equation of fractional order 1/λ at the origin. For integer m = 1/λ it can be solved in terms of Mittag-Leffler functions. In the last part, we derive Ward's equation for a general class of potentials as a tool to investigate universality. This allows us to determine the functional form of kernels that are translation invariant up to its integration domain.

show abstract

The boundary density profile of a Coulomb droplet. Freezing at the edge

Cited by 15 publications

References 55 publications

W-infinity symmetry in the quantum hall effect beyond the edge

W-infinity symmetry in the quantum hall effect beyond the edge

Scaling Limits of Planar Symplectic Ensembles

Scaling Limits of Planar Symplectic Ensembles

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