TY - JOUR

T1 - Theory of fermion liquids

AU - Kwon, H. J.

AU - Houghton, A.

AU - Marston, J. B.

N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 1995

Y1 - 1995

N2 - We develop a general theory of fermion liquids in spatial dimensions greater than 1. The principal method, bosonization, is applied to the cases of short- and long-range longitudinal interactions and to transverse gauge interactions. All the correlation funtions of the system may be obtained with the use of a generating functional. Short-range and Coulomb interactions do not destroy the Landau-Fermi fixed point. Non-Fermi liquid fixed points are found, however, in the cases of a super-long-range longitudinal interaction in two dimensions and transverse gauge interactions in two and three spatial dimensions. We consider in some detail the (2+1)-dimensional problem of a Chern-Simons gauge action combined with a longitudinal two-body interaction V(q)qy-1, which controls the density, and hence gauge, fluctuations. For y<0 we find that the gauge interaction is irrelevant and the Landau fixed point is stable, while for y>0 the interaction is relevant and the fixed point cannot be accessed by bosonization. Of special importance is the case y=0 (Coulomb interaction), which describes the Halperin-Lee-Read theory of the half-filled Landau level. We obtain the full quasiparticle propagator, which is of a marginal Fermi-liquid form. Using Ward identities, we show that neither the inclusion of nonlinear terms in the fermion dispersion nor vertex corrections alters our results: the fixed point is accessible by bosonization. As the two-point fermion Green's function is not gauge invariant, we also invetigate the gauge-invariant density response function. Near momentum Q=2kF, in addition to the Kohn anomaly we find other nonanalytic behavior. In the appendies we present a numerical calculation of the spectral function for a Fermi liquid with Landau parameter f00. We also show how Kohn's theorem is satisfied within the bosonization framework.

AB - We develop a general theory of fermion liquids in spatial dimensions greater than 1. The principal method, bosonization, is applied to the cases of short- and long-range longitudinal interactions and to transverse gauge interactions. All the correlation funtions of the system may be obtained with the use of a generating functional. Short-range and Coulomb interactions do not destroy the Landau-Fermi fixed point. Non-Fermi liquid fixed points are found, however, in the cases of a super-long-range longitudinal interaction in two dimensions and transverse gauge interactions in two and three spatial dimensions. We consider in some detail the (2+1)-dimensional problem of a Chern-Simons gauge action combined with a longitudinal two-body interaction V(q)qy-1, which controls the density, and hence gauge, fluctuations. For y<0 we find that the gauge interaction is irrelevant and the Landau fixed point is stable, while for y>0 the interaction is relevant and the fixed point cannot be accessed by bosonization. Of special importance is the case y=0 (Coulomb interaction), which describes the Halperin-Lee-Read theory of the half-filled Landau level. We obtain the full quasiparticle propagator, which is of a marginal Fermi-liquid form. Using Ward identities, we show that neither the inclusion of nonlinear terms in the fermion dispersion nor vertex corrections alters our results: the fixed point is accessible by bosonization. As the two-point fermion Green's function is not gauge invariant, we also invetigate the gauge-invariant density response function. Near momentum Q=2kF, in addition to the Kohn anomaly we find other nonanalytic behavior. In the appendies we present a numerical calculation of the spectral function for a Fermi liquid with Landau parameter f00. We also show how Kohn's theorem is satisfied within the bosonization framework.

UR - http://www.scopus.com/inward/record.url?scp=6244226876&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=6244226876&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.52.8002

DO - 10.1103/PhysRevB.52.8002

M3 - Article

AN - SCOPUS:6244226876

VL - 52

SP - 8002

EP - 8027

JO - Physical Review B

JF - Physical Review B

SN - 0163-1829

IS - 11

ER -