scholarly journals A TWO–DIMENSIONAL ELECTRON–HOLE SYSTEM UNDER THE INFLUENCE OF THE CHERN–SIMONS GAUGE FIELD CREATED BY QUANTUM POINT VORTICES

2021 ◽  
Vol 20 (1) ◽  
pp. 7-34
Author(s):  
Sveatoslav A. Moskalenko ◽  
◽  
Vsevolod A. Moskalenko ◽  
Igor V. Podlesny ◽  
Michael A. Liberman ◽  
...  
Keyword(s):  
Gauge Field ◽  
Field Approximation ◽  
New Physics ◽  
Point Vortices ◽  
Mean Field Approximation ◽  
Hole Density ◽  
Two Dimensional ◽  
Electron Hole ◽  
Quantum Point ◽  
Chern Simons

In the present work, the Chern–Simons (CS) gauge field theory developed by Jackiw and Pi [8] and widely used to interpret the fractional quantum Hall effects, is applied to describe a two-dimensional (2D) electron–hole (e–h) system in a strong perpendicular magnetic field and under the influence of quantum point vortices creating the CS gauge field. Composite particles formed by electrons and holes with equal integer positive numbers  of attached quantum point vortices are described by dressed field operators, which obey the Fermi or Bose statistics depending on even or odd numbers  . It is shown that the phase operators, as well as the vector and scalar potentials of the CS gauge field, depend on the difference between the electron and hole density operators. They vanish in the mean field approximation, when the average values of electron and hole densities coincide. Nevertheless, even in this case, the quantum fluctuations of the CS gauge field lead to new physics of the 2D e–h system.

scholarly journals Symmetry-resolved entanglement in AdS3/CFT2 coupled to U(1) Chern-Simons theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Suting Zhao ◽  
Christian Northe ◽  
René Meyer
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Gauge Field ◽  
Wilson Line ◽  
Entanglement Entropy ◽  
Simons Theory ◽  
Two Dimensional ◽  
Conformal Field ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We consider symmetry-resolved entanglement entropy in AdS3/CFT2 coupled to U(1) Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS3, namely the Ryu-Takayanagi geodesic minimally coupled to the U(1) Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged U(1) vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the U(1) Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincaré patch and global AdS3, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level k, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody type. Employing the $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.

Two Dimensional Bright and Dark Magnetoexcitons Interacting with Quantum Point Vortices

2019 ◽  
Vol 53 (16) ◽  
pp. 2055-2059
Author(s):  
S. A. Moskalenko ◽  
V. A. Moskalenko ◽  
I. V. Podlesny ◽  
I. A. Zubac
Keyword(s):  
Point Vortices ◽  
Two Dimensional ◽  
Quantum Point

Critical indices for spin correlation functions in ferromagnetic films

1979 ◽  
Vol 57 (10) ◽  
pp. 1686-1698 ◽  
Author(s):  
G. Gumbs ◽  
A. Griffin
Keyword(s):  
Correlation Functions ◽  
Finite Thickness ◽  
Mean Field ◽  
Spin Correlation ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Dimensional System ◽  
Two Dimensional ◽  
Critical Indices ◽  
The Mean

Using the Ginzburg–Landau–Wilson (GLW) Hamiltonian, we obtain, with the mean-field approximation, explicit expressions for the spin–spin correlation function χ(z,z′) of a film of thickness L above the phase transition temperature Tc and the spontaneous magnetization [Formula: see text] below Tc. The boundaries are treated using a temperature-independent extrapolation length Λ. From our results, we verify explicitly that for finite L, the critical indices associated with the spin–spin correlation functions and the surface magnetization are identical with those for the analogous two-dimensional system, for both the ordinary (Λ > 0) and surface (Λ < 0) transitions. Our model results nicely exhibit the fact that as long as L is finite, when the temperature T approaches sufficiently close to Tc, there is a crossover from behaviour characteristic of a single surface to two-dimensional behaviour. Within the one-loop, Hartree self-consistent field approximation, we study the effects of mode–mode coupling on the surface layer susceptibility in films of varying thicknesses. The singular behaviour obtained in the mean-field approximation is found to be completely removed in systems of finite thickness, the susceptibilities only exhibiting a finite cusp at the transition.

QUANTUM FLUCTUATIONS ENHANCE SUPERFLUIDITY IN TWO-DIMENSIONAL WEAKLY INTERACTING BOSON SYSTEM

2012 ◽  
Vol 26 (17) ◽  
pp. 1250107 ◽  
Author(s):  
PEI-SONG HE ◽  
WEN-LONG YOU
Keyword(s):  
Renormalization Group ◽  
Chemical Potential ◽  
Field Approximation ◽  
High Energy ◽  
Superfluid Density ◽  
Energy Scale ◽  
Mean Field Approximation ◽  
Two Dimensional ◽  
Boson System ◽  
Weakly Interacting

In the present paper, we compute the superfluid density of two-dimensional weakly interacting boson system at zero temperature using one-loop renormalization group calculations under the scheme of newly derived formula [M. Holzmann and G. Baym Phy. Rev. B 76, 092502 (2007)]. We find that the interactions between the boson particles are marginally irrelevant in the renormalization group sense. The fluctuations of high-energy scale enhance superfluid density compared with the result of the mean-field approximation. The correction has ( ln μ) form, where μ is the chemical potential of the boson system.

scholarly journals Regularized vortex approximation for 2D Euler equations with transport noise

2020 ◽  
Vol 20 (06) ◽  
pp. 2040002
Author(s):  
Michele Coghi ◽  
Mario Maurelli
Keyword(s):  
Euler Equations ◽  
Mean Field ◽  
Field Approximation ◽  
Point Vortices ◽  
Mean Field Approximation ◽  
Vorticity Equation ◽  
Suitable Function ◽  
Common Noise ◽  
2D Euler Equations ◽  
Number Of Particles

We study a mean field approximation for the 2D Euler vorticity equation driven by a transport noise. We prove that the Euler equations can be approximated by interacting point vortices driven by a regularized Biot–Savart kernel and the same common noise. The approximation happens by sending the number of particles [Formula: see text] to infinity and the regularization [Formula: see text] in the Biot–Savart kernel to [Formula: see text], as a suitable function of [Formula: see text].

Coupled Electron-Hole Transport: Beyond the Mean Field Approximation

1995 ◽  
Vol 74 (16) ◽  
pp. 3245-3248 ◽  
Author(s):  
L. Świerkowski ◽  
J. Szymański ◽  
Z. W. Gortel
Keyword(s):  
Mean Field ◽  
Field Approximation ◽  
Hole Transport ◽  
Mean Field Approximation ◽  
Electron Hole ◽  
The Mean

scholarly journals Collective in-plane magnetization in a two-dimensional XY macrospin system within the framework of generalized Ott–Antonsen theory

2020 ◽  
Vol 378 (2171) ◽  
pp. 20190259 ◽  
Author(s):  
Irina V. Tyulkina ◽  
Denis S. Goldobin ◽  
Lyudmila S. Klimenko ◽  
Igor S. Poperechny ◽  
Yuriy L. Raikher
Keyword(s):  
Magnetic Moments ◽  
Mean Field ◽  
Ferromagnetic State ◽  
Dipole Interaction ◽  
Field Approximation ◽  
Square Lattice ◽  
Mean Field Approximation ◽  
Two Dimensional ◽  
Stripe Structure ◽  
First Order Phase

The problem of magnetic transitions between the low-temperature (macrospin ordered) phases in two-dimensional XY arrays is addressed. The system is modelled as a plane structure of identical single-domain particles arranged in a square lattice and coupled by the magnetic dipole–dipole interaction; all the particles possess a strong easy-plane magnetic anisotropy. The basic state of the system in the considered temperature range is an antiferromagnetic (AF) stripe structure, where the macrospins (particle magnetic moments) are still involved in thermofluctuational motion: the superparamagnetic blocking T b temperature is lower than that ( T af ) of the AF transition. The description is based on the stochastic equations governing the dynamics of individual magnetic moments, where the interparticle interaction is added in the mean-field approximation. With the technique of a generalized Ott–Antonsen theory, the dynamics equations for the order parameters (including the macroscopic magnetization and the AF order parameter) and the partition function of the system are rigorously obtained and analysed. We show that inside the temperature interval of existence of the AF phase, a static external field tilted to the plane of the array is able to induce first-order phase transitions from AF to ferromagnetic state; the phase diagrams displaying stable and metastable regions of the system are presented. This article is part of the theme issue ‘Patterns in soft and biological matters’.

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