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 twodimensional square lattice. Using a recently derived JordanWigner transformation, I map this problem onto a gas of fermions on the same lattice coupled to a ChernSimons 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 saddlepoint 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 »
 Authors:

 Department of Physics, University of Illinois at UrbanaChampaign, 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 01631829
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; HIGHTC SUPERCONDUCTORS; HALL EFFECT; MEISSNEROCHSENFELD EFFECT; LAGRANGIAN FUNCTION; MAGNETIC FLUX; TWODIMENSIONAL 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 twodimensional square lattice. Using a recently derived JordanWigner transformation, I map this problem onto a gas of fermions on the same lattice coupled to a ChernSimons 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 saddlepoint 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 lowenergy 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 zerotemperature 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 = {01631829},
number = ,
volume = 42:1,
place = {United States},
year = {1990},
month = {7}
}