Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Modern Physics B

ANYON SUPERCONDUCTIVITY BEYOND THE RANDOM PHASE APPROXIMATION

Dmitri V. Khveshchenko, Ian I. Kogan

Published Aug 20, 1991• 2 citations
Publisher

Abstract

We carry out a revision of the mechanism of anyon superconductivity found in the Random Phase Approximation. It is shown that the Debye screening of a statistical Coulomb-like interaction produced by contributions beyond the RPA destroys the abovementioned mechanism. The linear mode appeared in the particle-hole channel within the RPA is identified with a finite damping zero-sound. As an alternative mechanism an attraction of anyons which could lead to a formation of boson composites is observed. A finite temperature phase transition, hydrodynamics and electrodynamics of anyon system are described from this alternative point of view.

DOI
10.1142/s0217979291000924

Related papers

Bosonization of 2D Fermions due to Spin and Statistical Magnetic Field Coupling and Possible Nature of Superconductivity and Pseudogap Phases Below E_g

B. Abdullaev, Chul Hong Park

A ground state energy variational calculation of anyon gas with Hamiltonian included the interaction of spins of particles with anyon vector potential induced, i.e. statistical, magnetic field exhibits exact cancelation of terms connected with fractional statistics. This leads to bosonization of anyons due to coupling of their spins with statistical magnetic field. We presume that at the dense gas fluctuations of effective spins destroy the coupling and bosons become anyons. At the assumption that pseudogap (PG) boundary is temperature independent and when anyons are fermions we use this model to interpret experimental phase diagrams of Tallon and Loram hole and electron doped High-T_c superconductors below PG energy E_g and find the qualitative and quantitative agreement. We do the hypothesis that phase transition (PT) of bosons into Bose-Einstein condensate is not of second order, but of first order, close to second one, PG regime is meta stable phase of bosons, and E_g=0 is the critical point of this PT. Bosons undergo PT into fermions on PG boundary. Described in the literature non-Fermi quasi-particles might be related to bosons with effective spins.

arXiv:cond-mat/0404668•Journal of the Korean Physical Society•Apr 28, 2004•3 citations

Correlated random-phase-approximation study of an anyon gas

Bob Liu, X. Q. Wang, Larry McLerran

The correlated random-phase-approximation (CRPA) method is applied to study the ground-state and excited-state properties of an anyon gas. We perform a systematic 1/N expansion to the calculation of elementary excitations, where N is the statistical parameter. We find that the leading-(1/N)-order contributions are the same as those obtained by calculations of the RPA response functions. We then consider corrections to the RPA by a perturbation of the exchange interactions, and show that these higher-order corrections are important at large wave vectors. Our calculation gives an excitation spectrum in good agreement with that obtained by the exact solution of a small system.

Physical review. B, Condensed matter•Jun 1, 1991•2 citations

TRANSPORT PROPERTIES OF ANYONS

Dmitri V. Khveshchenko

We consider electromagnetic response as well as electrical and thermal transport in a normal state of anyon system at finite temperatures. We find the frequency and momentum dependences of electrical and thermal conductivities in the longwavelength limit. It is also shown that a pole of electric current and stress tensor correlation functions identified at zero temperature with a gapless sound-like mode becomes a diffusion above the critical temperature of the hypothetical superfluid anyon phase transition.

International Journal of Modern Physics B•Sep 10, 1992•0 citations

Crossover from Cooper pairs to composite bosons: A generalized RPA analysis of collective excitations

Lotfi Belkhir, Mohit Randeria

We study the evolution of the ground state and the excitation spectrum of the two- and three-dimensional attractive (negative-U) Hubbard model as the system evolves from a Cooper-pair regime for U\ensuremath{\ll}t, to a composite boson regime for U\ensuremath{\gg}t. Our work is motivated by the observation that the high-temperature superconductors, with their short coherence lengths and unusual normal-state properties, may be in an intermediate coupling regime between these two limits. A mean-field analysis of pairing, suitably generalized to account for a shift in the chemical potential, is known to be able to describe the ground-state crossover as a function of U/t. We compute the collective-mode spectrum using a generalized random-phase-approximation analysis within the equations-of-motion formalism. We find a smooth evolution of the Anderson mode for weak coupling into the Bogoliubov sound mode for hard-core bosons. We then include a long-range Coulomb interaction and show that it leads to a plasmon which again evolves smoothly from weak to strong coupling.

arXiv:cond-mat/9310021•Physical review. B, Condensed matter•Mar 1, 1994•64 citations

Superfluid and Insulating Phases in an Interacting-Boson Model: Mean-Field Theory and the RPA

K. Sheshadri, H. R. Krishnamurthy, Rahul Anil Pandit +1 more

The bosonic Hubbard model is studied via a simple mean-field theory. At zero temperature, in addition to yielding a phase diagram that is qualitatively correct, namely a superfluid phase for non-integer fillings and a Mott transition from a superfluid to an insulating phase for integer fillings, this theory gives results that are in good agreement with Monte Carlo simulations. In particular, the superfluid fraction obtained as a function of the interaction strength U for both integer and non-integer fillings is close to the simulation results. In all phases the excitation spectra are obtained by using the random phase approximation (RPA): the spectrum has a gap in the insulating phase and is gapless (and linear at small wave vectors) in the superfluid phase. Analytic results are presented in the limits of large U and small superfluid density. Finite-temperature phase diagrams and the Mott-insulator-normal-phase crossover are also described.

Europhysics Letters (EPL)•May 1, 1993•428 citations

An Evaluation of Collective Mode in Weak and Strong Coupling Limit of One-Dimensional Fermi Gas

Shreemant Raman, L. K. Mishra

In this paper, we have studied the one-dimensional Fermi gas with attractive δ interaction potential in the quasi-particle random phase approximation at zero temperature. Using the theoretical formalism of Alm and Schuck, we have studied the behavior of collective modes over the whole coupling regime from weak coupling (high density) to strong coupling (low density). We observe that in the weak- coupling limit particle-hole RPA is approached to low momenta and the collective mode in the strong coupling limit reproduces the Bogoliubov mode for the weakly interacting bosons.

International Journal of Chemical Sciences•Jan 1, 2011•0 citations
We carry out a revision of the mechanism of anyon superconductivity found in the Random Phase Approximation. It is shown that the Debye screening of a statistical Coulomb-like interaction produced by contributions beyond the RPA destroys the abovementioned mechanism. The linear mode appeared in the particle-hole channel within the RPA is identified with a finite damping zero-sound. As an alternative mechanism an attraction of anyons which could lead to a formation of boson composites is observed. A finite temperature phase transition, hydrodynamics and electrodynamics of anyon system are described from this alternative point of view.
A ground state energy variational calculation of anyon gas with Hamiltonian included the interaction of spins of particles with anyon vector potential induced, i.e. statistical, magnetic field exhibits exact cancelation of terms connected with fractional statistics. This leads to bosonization of anyons due to coupling of their spins with statistical magnetic field. We presume that at the dense gas fluctuations of effective spins destroy the coupling and bosons become anyons. At the assumption that pseudogap (PG) boundary is temperature independent and when anyons are fermions we use this model to interpret experimental phase diagrams of Tallon and Loram hole and electron doped High-T_c superconductors below PG energy E_g and find the qualitative and quantitative agreement. We do the hypothesis that phase transition (PT) of bosons into Bose-Einstein condensate is not of second order, but of first order, close to second one, PG regime is meta stable phase of bosons, and E_g=0 is the critical point of this PT. Bosons undergo PT into fermions on PG boundary. Described in the literature non-Fermi quasi-particles might be related to bosons with effective spins.
The correlated random-phase-approximation (CRPA) method is applied to study the ground-state and excited-state properties of an anyon gas. We perform a systematic 1/N expansion to the calculation of elementary excitations, where N is the statistical parameter. We find that the leading-(1/N)-order contributions are the same as those obtained by calculations of the RPA response functions. We then consider corrections to the RPA by a perturbation of the exchange interactions, and show that these higher-order corrections are important at large wave vectors. Our calculation gives an excitation spectrum in good agreement with that obtained by the exact solution of a small system.
We consider electromagnetic response as well as electrical and thermal transport in a normal state of anyon system at finite temperatures. We find the frequency and momentum dependences of electrical and thermal conductivities in the longwavelength limit. It is also shown that a pole of electric current and stress tensor correlation functions identified at zero temperature with a gapless sound-like mode becomes a diffusion above the critical temperature of the hypothetical superfluid anyon phase transition.
We study the evolution of the ground state and the excitation spectrum of the two- and three-dimensional attractive (negative-U) Hubbard model as the system evolves from a Cooper-pair regime for U\ensuremath{\ll}t, to a composite boson regime for U\ensuremath{\gg}t. Our work is motivated by the observation that the high-temperature superconductors, with their short coherence lengths and unusual normal-state properties, may be in an intermediate coupling regime between these two limits. A mean-field analysis of pairing, suitably generalized to account for a shift in the chemical potential, is known to be able to describe the ground-state crossover as a function of U/t. We compute the collective-mode spectrum using a generalized random-phase-approximation analysis within the equations-of-motion formalism. We find a smooth evolution of the Anderson mode for weak coupling into the Bogoliubov sound mode for hard-core bosons. We then include a long-range Coulomb interaction and show that it leads to a plasmon which again evolves smoothly from weak to strong coupling.
The bosonic Hubbard model is studied via a simple mean-field theory. At zero temperature, in addition to yielding a phase diagram that is qualitatively correct, namely a superfluid phase for non-integer fillings and a Mott transition from a superfluid to an insulating phase for integer fillings, this theory gives results that are in good agreement with Monte Carlo simulations. In particular, the superfluid fraction obtained as a function of the interaction strength U for both integer and non-integer fillings is close to the simulation results. In all phases the excitation spectra are obtained by using the random phase approximation (RPA): the spectrum has a gap in the insulating phase and is gapless (and linear at small wave vectors) in the superfluid phase. Analytic results are presented in the limits of large U and small superfluid density. Finite-temperature phase diagrams and the Mott-insulator-normal-phase crossover are also described.
In this paper, we have studied the one-dimensional Fermi gas with attractive δ interaction potential in the quasi-particle random phase approximation at zero temperature. Using the theoretical formalism of Alm and Schuck, we have studied the behavior of collective modes over the whole coupling regime from weak coupling (high density) to strong coupling (low density). We observe that in the weak- coupling limit particle-hole RPA is approached to low momenta and the collective mode in the strong coupling limit reproduces the Bogoliubov mode for the weakly interacting bosons.