TY - JOUR

T1 - Crossover and scaling in a nearly antiferromagnetic Fermi liquid in two dimensions

AU - Sachdev, Subir

AU - Chubukov, Andrey V.

AU - Sokol, Alexander

PY - 1995

Y1 - 1995

N2 - We consider two-dimensional Fermi liquids in the vicinity of a quantum transition to a phase with commensurate, antiferromagnetic long-range order. Depending upon the Fermi-surface topology, mean-field spin-density-wave theory predicts two different types of such transitions, with mean-field dynamic critical exponents z=1 (when the Fermi surface does not cross the magnetic zone boundary, type A) and z=2 (when the Fermi surface crosses the magnetic zone boundary, type B). The type-A system only displays z=1 behavior at all energies and its scaling properties are similar (though not identical) to those of an insulating Heisenberg antiferromagnet. Under suitable conditions precisely stated in this paper, the type-B system displays a crossover from relaxational behavior at low energies to type-A behavior at high energies. A scaling hypothesis is proposed to describe this crossover: we postulate a universal scaling function which determines the entire, temperature-, wave-vector-, and frequency-dependent, dynamic, staggered spin susceptibility in terms of four experimentally measurable, T=0 parameters. The scaling function contains the full scaling behavior in all regimes for both type-A and -B systems. The crossover behavior of the uniform susceptibility and the specific heat is somewhat more complicated and is also discussed. Explicit computation of the crossover functions is carried out in a large N expansion on a mean-field model. Some new results for the critical properties on the ordered side of the transition are also obtained in a spin-density-wave formalism. The possible relevance of our results to the doped cuprate compounds is briefly discussed.

AB - We consider two-dimensional Fermi liquids in the vicinity of a quantum transition to a phase with commensurate, antiferromagnetic long-range order. Depending upon the Fermi-surface topology, mean-field spin-density-wave theory predicts two different types of such transitions, with mean-field dynamic critical exponents z=1 (when the Fermi surface does not cross the magnetic zone boundary, type A) and z=2 (when the Fermi surface crosses the magnetic zone boundary, type B). The type-A system only displays z=1 behavior at all energies and its scaling properties are similar (though not identical) to those of an insulating Heisenberg antiferromagnet. Under suitable conditions precisely stated in this paper, the type-B system displays a crossover from relaxational behavior at low energies to type-A behavior at high energies. A scaling hypothesis is proposed to describe this crossover: we postulate a universal scaling function which determines the entire, temperature-, wave-vector-, and frequency-dependent, dynamic, staggered spin susceptibility in terms of four experimentally measurable, T=0 parameters. The scaling function contains the full scaling behavior in all regimes for both type-A and -B systems. The crossover behavior of the uniform susceptibility and the specific heat is somewhat more complicated and is also discussed. Explicit computation of the crossover functions is carried out in a large N expansion on a mean-field model. Some new results for the critical properties on the ordered side of the transition are also obtained in a spin-density-wave formalism. The possible relevance of our results to the doped cuprate compounds is briefly discussed.

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U2 - 10.1103/PhysRevB.51.14874

DO - 10.1103/PhysRevB.51.14874

M3 - Article

AN - SCOPUS:0000481319

SN - 0163-1829

VL - 51

SP - 14874

EP - 14891

JO - Physical Review B

JF - Physical Review B

IS - 21

ER -