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.

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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