Singular Behaviour of Electrons and of Composite Fermions in a Finite Effective Field

Hold temporarily. Revised version in progress

Taking into account the transverse gauge field fluctuations, which interact with composite fermions, we examine the finite temperature compressibility of the fermions as a function of an effective magnetic field $\Delta B = B - 2 n_e hc/e$ ($n_e$ is the density of electrons) near the half-filled state. It is shown that, after including the lowest order gauge field correction, the compressibility goes as ${\partial n \over \partial \mu} \propto e^{- \Delta \omega_c / 2 T} \lef...

An introductory survey of the theoretical ideas and calculations and the experimental results which depart from Landau Fermi-liquids is presented. Common themes and possible routes to the singularities leading to the breakdown of Landau Fermi liquids are categorized following an elementary discussion of the theory. Soluble examples of Singular Fermi liquids (often called Non-Fermi liquids) include models of impurities in metals with special symmetries and one-dimensional inte...

We present extensive comparisons of the composite fermion theory with exact results in the filling factor range $2/5>\nu>1/3$, which affirm that the composite fermion theory correctly describes the qualitative reorganization of the low energy Hilbert space of the strongly correlated electrons, and predicts eigenenergies with an accuracy of $\sim 0.1$ %. These facts establish the basic validity of the composite fermion description in this filling factor region.

We study the dephasing of fermions interacting with a fluctuating transverse gauge field. The divergence of the imaginary part of the fermion self energy at finite temperatures is shown to result from a breakdown of Fermi's golden rule due to a faster than exponential decay in time. The strong dephasing affects experiments where phase coherence is probed. This result is used to describe the suppression of Shubnikov-de Haas (SdH) oscillations of composite fermions (oscillation...

In this paper, we propose a gauge-invariant way to define and calculate the effective mass for quasiparticles in systems with gauge interactions, and apply it to a model closely related to the half-filled Landau level problem. Our model is equivalent to the Halperin-Lee-Read $\nu = 1/2$ Hamiltonian with an ultraviolet cutoff $\Lambda$ for the gauge fields, and we expand our answer in powers of $\Lambda / k_F$, assuming it is small. In this definition the effective mass depend...

We examine the problem of finite Fermi systems having a degenerate single-particle spectrum and show that the Landau approach, applied to such a system, admits the possibility of merging single-particle levels. It is demonstrated that the opportunity for this behavior is widespread in quantum many-body systems. The salient feature of the phenomenon is the occurrence of nonintegral quasiparticle occupation numbers, leading to a radical alteration of the standard quasiparticle ...

We construct a new representation of composite fermion wave functions in the lowest Landau level which enables Monte Carlo computations at arbitrary filling factors for a fairly large number of composite fermions, thus clearing the way toward a more detailed quantitative investigation of the fractional quantum Hall effect. As an illustrative application, thermodynamic estimates for the transport gaps of several spin polarized incompressible states have been obtained.

Fluctuations of the Chern-Simons gauge field in the composite Fermi liquid description of the half-filled Landau level are pair breaking in all angular momentum channels. For short-range electron-electron interactions these fluctuations are sufficiently strong to drive any T=0 pairing transition first order. For Coulomb interactions these fluctuations are weaker and a continuous transition is possible.

The definitions of the effective mass of the composite fermion are discussed for the half-filled Landau level problem. In a recent work, Shankar and Murthy show a finite effective mass of the composite fermion by a canonical transformation while the perturbative calculation gives the logarithmic divergence of the effective mass at the Fermi surface. We will emphasize that the different definition of the effective mass has the different physical processes. The finite one could...