2014/11/18 by Vladimir A. Zyuzin, Dmitrii L. Maslov
Mathematics · Physics and Astronomy · #Boson #Boundary (topology) #Condensed matter physics #Coupling (piping) #Fermion #Mathematical analysis #Mathematical physics #Mathematics #Omega #Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Spin (aerodynamics) #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.91.081102
published as Phys. Rev. B 91, 081102 (2015)
arxiv created 2014/11/18 · openalex publication_date 2015/02/04 · arxiv updated 2015/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We revisit the dynamic spin susceptibility \ensuremathχ(q,\ensuremathω) of one-dimensional interacting fermions. To second order in the interaction, backscattering results in a logarithmic correction to \ensuremathχ(q,\ensuremathω) at q\ensuremath≪kF, even if the single-particle spectrum is linearized near the Fermi points. Consequently, the dynamic spin structure factor Im\ensuremathχ(q,\ensuremathω) 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 Im\ensuremathχ(q,\ensuremathω) due to backscattering is larger than that due to finite mass by a factor of kF/q. We derive the renormalization group equations for the coupling constants of the g\ensuremath-ology model at finite \ensuremathω and q and find the corresponding expression for \ensuremathχ(q,\ensuremathω), valid to all orders in the interaction but not in the immediate vicinity of the continuum boundary, where the finite-mass effects become dominant.