TY - JOUR

T1 - Superfluidity of the lattice anyon gas and topological invariance

AU - Fradkin, Eduardo H

PY - 1990

Y1 - 1990

N2 - I consider a gas of free anyons with statistical parameter, 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 =1/2. 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 /. I consider the case in which an integer number of the Landau bands of the saddle-point problem are completely filled. If =/m and the density =r/q, with m, r, and q integers, the system is a superfluid, provided that q is larger than twice the largest common factor of m and r. If 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 and, 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.

AB - I consider a gas of free anyons with statistical parameter, 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 =1/2. 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 /. I consider the case in which an integer number of the Landau bands of the saddle-point problem are completely filled. If =/m and the density =r/q, with m, r, and q integers, the system is a superfluid, provided that q is larger than twice the largest common factor of m and r. If 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 and, 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.

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U2 - 10.1103/PhysRevB.42.570

DO - 10.1103/PhysRevB.42.570

M3 - Article

AN - SCOPUS:4243915989

SN - 0163-1829

VL - 42

SP - 570

EP - 586

JO - Physical Review B

JF - Physical Review B

IS - 1

ER -