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Title: Superfluidity of the lattice anyon gas and topological invariance

Abstract

I consider a gas of free'' anyons with statistical parameter {delta}, with hard cores, on a two-dimensional square lattice. Using a recently derived Jordan-Wigner transformation, I map this problem onto a gas of fermions on the same lattice coupled to a Chern-Simons gauge theory with coupling {theta}=1/2{delta}. At the semiclassical level, the system is found to be equivalent to a gas of fermions, with the same density, in an average effective magnetic field {rho}/{theta}. I consider the case in which an integer number of the Landau bands of the saddle-point problem are completely filled. If {delta}={pi}/{ital m} and the density {rho}={ital r}/{ital q}, with {ital m}, {ital r}, and {ital q} integers, the system is a superfluid, provided that {ital q} is larger than twice the largest common factor of {ital m} and {ital r}. If {ital q} is even and the system is half filled, the state may be either a superfluid or a quantum Hall phase. For all other values of {rho} and {delta}, compatible with integer filling of the Landau bands, the system is in a quantum Hall phase. The dynamical stability of the superfluid state is ensured by the topological invariance of the quantized Hall conductancemore » of the fermion problem. I find a close analogy between anyon superconductivity and the Schwinger mechanism. The effective Lagrangian for the low-energy modes coupled to the electromagnetic field is derived. The energies of fermion and flux states are logarithmically divergent, but finite for the anyon state. The system has flux quantization, a zero-temperature Hall effect with a quantized Hall conductance, Meissner effect, charged vortices, screening with induced magnetic fields for static charges, and different masses for the longitudinal and transverse components of the electromagnetic field.« less

Authors:
 [1]
  1. Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL (USA) Institute for Theoretical Physics, University of California at Santa Barbara, Santa Barbara, CA (USA)
Publication Date:
OSTI Identifier:
6781782
Resource Type:
Journal Article
Journal Name:
Physical Review, B: Condensed Matter; (USA)
Additional Journal Information:
Journal Volume: 42:1; Journal ID: ISSN 0163-1829
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; HIGH-TC SUPERCONDUCTORS; HALL EFFECT; MEISSNER-OCHSENFELD EFFECT; LAGRANGIAN FUNCTION; MAGNETIC FLUX; TWO-DIMENSIONAL CALCULATIONS; FUNCTIONS; SUPERCONDUCTORS; 656100* - Condensed Matter Physics- Superconductivity

Citation Formats

Fradkin, E. Superfluidity of the lattice anyon gas and topological invariance. United States: N. p., 1990. Web. doi:10.1103/PhysRevB.42.570.
Fradkin, E. Superfluidity of the lattice anyon gas and topological invariance. United States. doi:10.1103/PhysRevB.42.570.
Fradkin, E. Sun . "Superfluidity of the lattice anyon gas and topological invariance". United States. doi:10.1103/PhysRevB.42.570.
@article{osti_6781782,
title = {Superfluidity of the lattice anyon gas and topological invariance},
author = {Fradkin, E},
abstractNote = {I consider a gas of free'' anyons with statistical parameter {delta}, with hard cores, on a two-dimensional square lattice. Using a recently derived Jordan-Wigner transformation, I map this problem onto a gas of fermions on the same lattice coupled to a Chern-Simons gauge theory with coupling {theta}=1/2{delta}. At the semiclassical level, the system is found to be equivalent to a gas of fermions, with the same density, in an average effective magnetic field {rho}/{theta}. I consider the case in which an integer number of the Landau bands of the saddle-point problem are completely filled. If {delta}={pi}/{ital m} and the density {rho}={ital r}/{ital q}, with {ital m}, {ital r}, and {ital q} integers, the system is a superfluid, provided that {ital q} is larger than twice the largest common factor of {ital m} and {ital r}. If {ital q} is even and the system is half filled, the state may be either a superfluid or a quantum Hall phase. For all other values of {rho} and {delta}, compatible with integer filling of the Landau bands, the system is in a quantum Hall phase. The dynamical stability of the superfluid state is ensured by the topological invariance of the quantized Hall conductance of the fermion problem. I find a close analogy between anyon superconductivity and the Schwinger mechanism. The effective Lagrangian for the low-energy modes coupled to the electromagnetic field is derived. The energies of fermion and flux states are logarithmically divergent, but finite for the anyon state. The system has flux quantization, a zero-temperature Hall effect with a quantized Hall conductance, Meissner effect, charged vortices, screening with induced magnetic fields for static charges, and different masses for the longitudinal and transverse components of the electromagnetic field.},
doi = {10.1103/PhysRevB.42.570},
journal = {Physical Review, B: Condensed Matter; (USA)},
issn = {0163-1829},
number = ,
volume = 42:1,
place = {United States},
year = {1990},
month = {7}
}