Dynamic correlations in a one-dimensional fermionic liquid

Michael Pustilnik

School of Physics, Georgia Institute of Technology, Atlanta, USA

We evaluate the dynamic structure factor S(q,ω) of interacting one-dimensional spinless fermions with a nonlinear dispersion relation. Besides being of fundamental interest for its own sake, detailed knowledge of the structure factor is crucial for the description of the variety of effects that owe their existence to particle-hole asymmetry. The combined effect of the nonlinear dispersion and of the interactions leads to new universal features of S(q,ω). The main spectral weight of S(q,ω) is confined to a narrow frequency interval of the width
δω∼ q2/m. At the boundaries of this interval the structure factor exhibits power-law singularities. The singularities are similar in origin to the well-known Fermi-edge singularity in the X-ray absorption spectra of metals.

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