Lifetime of a one-dimensional fermion

ORAL

Abstract

Interaction between fermions in one dimension is usually accounted for within the exactly solvable Tomonaga-Luttinger model. The crucial simplification made in this model is the linearization of the fermionic spectrum. That simplification leads to an infinite lifetime of a fermion at the mass shell, i.e., the corresponding Green function $G(\varepsilon,\xi_k)$ diverges at $\varepsilon=\xi_k$. We find that inclusion of the curvature of electron spectrum, $\xi_k=v_Fk+k^2/2m$, yields a finite decay rate of a fermion, $1/\tau(\xi_k)\propto \theta(k)k^8/m^3$; here for definiteness we consider right-moving particles, and $k$ is measured from the Fermi wave vector. The found finite lifetime allows one to assess the limitations of the Luttinger liquid paradigm.

*NSF, Grants No. DMR02-37296, No. DMR-0405212, No. EIA02-10736, and A. P. Sloan Foundation.

–

Authors

  • Maxim Khodas

    • William I. Fine Theoretical Physics Institute and School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA

  • Iddo Ussishkin

    • Intel Corp., Israel

  • Michael Pustilnik

    • Georgia Institute of Technology
    • School of Physics, Georgia Institute of Technology,Atlanta, GA 30332

  • Alex Kamenev

    • William I. Fine Theoretical Physics Institute and School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA

  • Leonid Glazman

    • University of Minnesota
    • W.I. Fine Theoretical Physics Institute, University of Minnesota
    • William I. Fine Theoretical Physics Institute and School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA