For the interacting SSH model, QMC data show that the low-frequency response of chiral density to an electric field remains equal to the electrical conductivity, so local Hubbard interactions do not renormalize the 1D chiral effect.
Quantum Oscillations in the Chiral Magnetic Conductivity
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abstract
In strong magnetic field the longitudinal magnetoconductivity in 3D chiral materials is shown to exhibit a new type of quantum oscillations arising from the chiral magnetic effect (CME). These quantum CME oscillations are predicted to dominate over the Shubnikov-de Haas (SdH) ones in chiral materials with an approximately conserved chirality of quasiparticles at strong magnetic fields. The phase of quantum CME oscillations differs from the phase of the conventional SdH oscillations by $\pi/2$.
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Influence of interactions on the chiral effect in $1D$ Dirac semimetal
For the interacting SSH model, QMC data show that the low-frequency response of chiral density to an electric field remains equal to the electrical conductivity, so local Hubbard interactions do not renormalize the 1D chiral effect.