Violation of Wiedemann-Franz law in strongly interacting one-dimensional electrons

We present our study on the violation of Wiedemann-Franz law in one-dimensional strongly interacting spinless electron systems. The Luttinger liquid theory describes the low-energy excitations of a gapless one-dimensional quantum many-body systems. The defining feature of a Luttinger liquid is its well-behaved collective excitations, analogous to sound waves, with linear bosonic dispersion. However, real one-dimensional quantum systems demonstrate a non-linear interacting quantum liquid behavior that is different from either Luttinger liquids (1D) or Fermi liquids (2D). Further, such a system violates the Wiedemann Franz law (κ ∝ σΤ, where κ is the thermal conductance and σ is the electrical conductance). This is because any arbitrarily weak interaction potential between Luttinger liquid excitations leads to divergences in the scattering amplitude between Luttinger liquid excitatations. We adopt the one-dimensional Wigner crystal as the strongly interacting regime of Luttinger liquid and show that the violation of the Wiedemann-Franz law can be demonstrated by calculating the correction to thermal conductance due to scattering between bosonic excitations in the presence of a weak non-linearity in dispersion.