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arXiv:1411.4993 · Physical Review B

Dynamical spin structure factor of one-dimensional interacting fermions

Vladimir A. Zyuzin, Dmitrii L. Maslov

Published Feb 4, 2015• 3 citations
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Abstract

We revisit the dynamic spin susceptibility $\ensuremath{\chi}(q,\ensuremath{\omega})$ of one-dimensional interacting fermions. To second order in the interaction, backscattering results in a logarithmic correction to $\ensuremath{\chi}(q,\ensuremath{\omega})$ at $q\ensuremath{\ll}{k}_{F}$, even if the single-particle spectrum is linearized near the Fermi points. Consequently, the dynamic spin structure factor $\mathrm{Im}\ensuremath{\chi}(q,\ensuremath{\omega})$ is nonzero at frequencies above the single-particle continuum. In the boson language, this effect results from the marginally irrelevant backscattering operator of the sine-Gordon model. Away from the threshold, the high-frequency tail of $\mathrm{Im}\ensuremath{\chi}(q,\ensuremath{\omega})$ due to backscattering is larger than that due to finite mass by a factor of ${k}_{F}/q$. We derive the renormalization group equations for the coupling constants of the $g\ensuremath{-}\text{ology}$ model at finite $\ensuremath{\omega}$ and $q$ and find the corresponding expression for $\ensuremath{\chi}(q,\ensuremath{\omega})$, valid to all orders in the interaction but not in the immediate vicinity of the continuum boundary, where the finite-mass effects become dominant.

DOI
10.1103/physrevb.91.081102

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