We present an exact solution for the interacting electron gas in the half-filled lowest Landau level on a thin torus. The low energy sector consists of non-interacting, one-dimensional, neutral fermions (dipoles). The ground state, which is homogeneous, is the Fermi sea obtained by filling the negative energy states and the excited states are the gapless neutral excitations out of this one-dimensional sea. We identify this ground state as a version of the Rezayi-Read state, and find that it develops continuously, as the circumference grows, into the Rezayi-Read state that is believed to describe the observed metallic phase in the two-dimensional system. This suggests a Luttinger liquid description of the half-filled Landau level.We present an exact solution for the interacting electron gas in the half-filled lowest Landau level on a thin torus. The low energy sector consists of non-interacting, one-dimensional, neutral fermions (dipoles). The ground state, which is homogeneous, is the Fermi sea obtained by filling the negative energy states and the excited states are the gapless neutral excitations out of this one-dimensional sea. We identify this ground state as a version of the Rezayi-Read state, and find that it develops continuously, as the circumference grows, into the Rezayi-Read state that is believed to describe the observed metallic phase in the two-dimensional system. This suggests a Luttinger liquid description of the half-filled Landau level.

Bulletin of the American Physical SocietyMar 15, 20060 citations

Landau Fermi-liquid theory

Piers Coleman

Cambridge University Press eBooksNov 26, 201518 citations

Fermi-liquid-like state in a half-filled Landau level

Edward H. Rezayi, N. Read

A system of electrons in a half-filled Landau level is investigated in spherical geometry. For systems of size from N=1 to 14 electrons with flux ${\mathit{N}}_{\mathrm{\ensuremath{\varphi}}}$=2(N-1) the angular momentum of the ground state is as predicted by Hund's second rule for composite fermions of one electron and two vortices at zero magnetic field. Low lying excitations also fit this interpretation and trial wave functions give excellent overlaps. The two-particle correlation function shows a significant correlation hole at short distances and suggests an asymptotically oscillating form at long distances, as in a Fermi liquid.A system of electrons in a half-filled Landau level is investigated in spherical geometry. For systems of size from N=1 to 14 electrons with flux ${\mathit{N}}_{\mathrm{\ensuremath{\varphi}}}$=2(N-1) the angular momentum of the ground state is as predicted by Hund's second rule for composite fermions of one electron and two vortices at zero magnetic field. Low lying excitations also fit this interpretation and trial wave functions give excellent overlaps. The two-particle correlation function shows a significant correlation hole at short distances and suggests an asymptotically oscillating form at long distances, as in a Fermi liquid.

Physical Review LettersFeb 7, 1994224 citations

Does a Fermi liquid on a half-filled Landau level have Pomeranchuk instabilities?

Jorge Quintanilla, Orion Ciftja

We present a theory of spontaneous Fermi surface deformations for half-filled Landau levels (filling factors of the form $ν=2n+1/2$ ). We assume the half-filled level to be in a compressible, Fermi liquid state with a circular Fermi surface. The Landau level projection is incorporated via a modified effective electron-electron interaction and the resulting band structure is described within the Hartree-Fock approximation. We regulate the infrared divergences in the theory and probe the intrinsic tendency of the Fermi surface to deform through Pomeranchuk instabilities. We find that the corresponding susceptibility never diverges, though the system is asymptotically unstable in the $n \to \infty$ limit.We present a theory of spontaneous Fermi surface deformations for half-filled Landau levels (filling factors of the form $ν=2n+1/2$). We assume the half-filled level to be in a compressible, Fermi liquid state with a circular Fermi surface. The Landau level projection is incorporated via a modified effective electron-electron interaction and the resulting band structure is described within the Hartree-Fock approximation. We regulate the infrared divergences in the theory and probe the intrinsic tendency of the Fermi surface to deform through Pomeranchuk instabilities. We find that the corresponding susceptibility never diverges, though the system is asymptotically unstable in the $n \to \infty$ limit.

arXiv:0904.0658Apr 4, 20090 citations

Landau theory of Fermi liquids reformulated

Ch.G. van Weert, M.C.J. Leermakers, Adriaan M. J. Schakel

Physica A Statistical Mechanics and its ApplicationsOct 1, 19865 citations

We present a theory of spontaneous Fermi surface deformations for half-filled Landau levels (filling factors of the form

ν=2n+1/2

). We assume the half-filled level to be in a compressible, Fermi liquid state with a circular Fermi surface. The Landau level projection is incorporated via a modified effective electron-electron interaction and the resulting band structure is described within the Hartree-Fock approximation. We regulate the infrared divergences in the theory and probe the intrinsic tendency of the Fermi surface to deform through Pomeranchuk instabilities. We find that the corresponding susceptibility never diverges, though the system is asymptotically unstable in the

n \to \infty

limit.