A Generalization of the Stillinger–Lovett Sum Rules for the Two-Dimensional Jellium

Šamaj, L.

doi:10.1007/s10955-007-9376-z

Cited by 8 publications

(12 citation statements)

References 22 publications

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“…Therefore, we get the zeroth moment 19) in agreement with equation (1.20) in [1], and the part linear in Z of the second moment (2.1). It may be remarked that the k 4 term of (2.18) is related to the compressibility, which is exactly known only for the 2D OCP [5].…”

Section: Another Derivationsupporting

confidence: 78%

“…One can obtain the last result in an alternative way by considering the charge density induced around the guest charge [1] ρ(r|Ze, 0) = −Ze κ 2 2π K 0 (κr). (4.12)…”

Section: High-temperature Limitmentioning

confidence: 99%

“…All potential moments are available for the present system due to the knowledge of the induced charge density around the guest charge [18,1]:…”

Section: One-component Plasma At βE 2 =mentioning

confidence: 99%

“…Š.) has derived a generalization of the Stillinger-Lovett sum rule for a guest charge immersed in a two-dimensional one-component plasma [1]: an exact simple expression for the second moment of the screening cloud around the guest charge was obtained, by using a mapping technique onto a discrete one-dimensional anticommuting-field theory. In the present paper, we first show that the same result can be obtained in a simpler way by just using the BGY hierarchy, which provides also more general results.…”

Section: Introductionmentioning

confidence: 99%

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Guest Charge and Potential Fluctuations in Two-Dimensional Classical Coulomb Systems

Jancovici

Šamaj

2008

J Stat Phys

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A known generalization of the Stillinger-Lovett sum rule for a guest charge immersed in a two-dimensional one-component plasma (the second moment of the screening cloud around this guest charge) is more simply retrieved, just by using the BGY hierarchy for a mixture of several species; the zeroth moment of the excess density around a guest charge immersed in a two-component plasma is also obtained. The moments of the electric potential are related to the excess chemical potential of a guest charge; explicit results are obtained in several special cases.

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Section: Another Derivationsupporting

confidence: 78%

“…One can obtain the last result in an alternative way by considering the charge density induced around the guest charge [1] ρ(r|Ze, 0) = −Ze κ 2 2π K 0 (κr). (4.12)…”

Section: High-temperature Limitmentioning

confidence: 99%

“…All potential moments are available for the present system due to the knowledge of the induced charge density around the guest charge [18,1]:…”

Section: One-component Plasma At βE 2 =mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Guest Charge and Potential Fluctuations in Two-Dimensional Classical Coulomb Systems

Jancovici

Šamaj

2008

J Stat Phys

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“…This result goes back to [1]. The second moment is more involved [3,29,30]. Curiously, the second moment vanishes at ν = 1 3 and a = 1.…”

Section: Resultsmentioning

confidence: 65%

Collective field theory for quantum Hall states

2015

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We develop a collective field theory for fractional quantum Hall (FQH) states. We show that in the leading approximation for a large number of particles, the properties of Laughlin states are captured by a Gaussian free field theory with a background charge. Gradient corrections to the Gaussian field theory arise from the covariant ultraviolet regularization of the theory, which produces the gravitational anomaly. These corrections are described by a theory closely related to the Liouville theory of quantum gravity. The field theory simplifies the computation of correlation functions in FQH states and makes manifest the effect of quantum anomalies.PACS numbers: 73.43. Cd, 73.43.Lp, Introduction Since the work of Laughlin [1], a common approach to analyzing the physics of the fractional quantum Hall effect (FQHE) starts with a trial ground state wave function for N electrons. Despite its success, this approach is an impractical framework for studying the collective behavior of a large number of electrons ( N ∼ 10 6 , in samples exhibiting the QHE). As a result, some subtle properties of QHE states, such as the gravitational anomaly [2-10], were computed only recently.The effects of quantum anomalies are essential in the physics of the QHE. Although anomalies originate at short distances on the order of the magnetic length, they control the large-scale properties of the state, such as transport. It was recently shown in [10] that, like the Hall conductance, transport coefficients determined by the gravitational anomaly are expected to be quantized on QH plateaus. For this reason it is important to formulate the theory of QH effect in a fashion which makes the quantum anomalies manifest. The field theory approach seems the most appropriate for this purpose.In this paper, we develop a field theory for Laughlin states. This approach naturally captures universal features of the QHE, and emphasizes geometric aspects of QH-states. We demonstrate how the field theory encompasses recent developments in the field [2-10] and obtain some properties of quasi-hole excitations. Preliminary treatment of this approach appears in [3].The field theory framework uncovers a connection between the QHE and random geometry, specifically 2D Liouville quantum gravity. Since its introduction, the Laughlin wave function has been a practical model wave function mainly because of the plasma analogy. This analogy to a 2D statistical mechanical system allowed the most salient features of the state -uniform density and fractional quasi-hole charge -to be easily captured by a saddle point approach to the partition function of the equivalent plasma.Every analysis to date has stopped at the saddle point. as a result subtle features of the theory such as the gravitational anomaly were missed. We show how the Laughlin wave function maps to a full quantum field theory. This approach allows to go beyond the saddle point and

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Expanded Vandermonde Powers and Sum Rules for the Two-Dimensional One-Component Plasma

Téllez

Forrester

2012

J Stat Phys

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The two-dimensional one-component plasma (2dOCP) is a system of N mobile particles of the same charge q on a surface with a neutralising background. The Boltzmann factor of the 2dOCP at temperature T can be expressed as a Vandermonde determinant to the power Γ = q 2 /(k B T ). Recent advances in the theory of symmetric and anti-symmetric Jack polymonials provide an efficient way to expand this power of the Vandermonde in their monomial basis, allowing the computation of several thermodynamic and structural properties of the 2dOCP for N values up to 14 and Γ equal to 4, 6 and 8. In this work, we explore two applications of this formalism to study the moments of the pair correlation function of the 2dOCP on a sphere, and the distribution of radial linear statistics of the 2dOCP in the plane.

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A Generalization of the Stillinger–Lovett Sum Rules for the Two-Dimensional Jellium

Cited by 8 publications

References 22 publications

Guest Charge and Potential Fluctuations in Two-Dimensional Classical Coulomb Systems

Guest Charge and Potential Fluctuations in Two-Dimensional Classical Coulomb Systems

Collective field theory for quantum Hall states

Expanded Vandermonde Powers and Sum Rules for the Two-Dimensional One-Component Plasma

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