Bosonization of strongly interacting one-dimensional electrons

Abstract

Strong repulsive interactions in a one-dimensional electron system suppress the exchange coupling $J$ of electron spins to a value much smaller than the Fermi energy ${E}_{F}$. The conventional theoretical description of such systems based on the bosonization approach and the concept of Tomonaga-Luttinger liquid is applicable only at energies below $J$. In this paper, we develop a theoretical approach valid at all energies below the Fermi energy, including a broad range of energies between $J$ and ${E}_{F}$. The method involves bosonization of the charge degrees of freedom, while the spin excitations are treated exactly. We use this technique to calculate the spectral functions of strongly interacting electron systems at energies in the range $J⪡\ensuremath{\epsilon}⪡{E}_{F}$. We show that in addition to the expected features at the wave vector $k$ near the Fermi point ${k}_{F}$, the spectral function has a strong peak centered at $k=0$. Our theory also provides analytical description of the spectral function singularities near $3{k}_{F}$ (the ``shadow band'' features).