Dephasing in quasi-1D wires: Non-Markovian noise and correlations due to itinerant spin interactions

Motivated by the interest in many-body localization, we revisit the problem of dephasing due to electron-electron scattering in quasi-1D (many channel) wires. The effectively Markovian bath due to Coulomb interactions dephases at any nonzero temperature [1]. The effect of short-ranged (e.g. spin exchange) electron-electron scattering is more subtle. The latter induces a non-Markovian, diffusive noise kernel. Formally the field theory describing the dephasing in the presence of a purely diffusive bath has an upper critical spatial dimension of d = 4, and is strongly coupled in d = 1 [2]. We show that a perturbative expansion in the diffusive noise kernel is well-defined but unphysical at long times. We also consider the case of both Coulomb and spin-exchange scattering, using the former to physically regularize the latter. In this case we find "rephasing" contributions at second order that are in contrast to the Markovian limit [3]. We discuss possible experimental signatures.
[1] B. L. Altshuler, A. G. Aronov, and D. E. Khmelnitsky, J. Phys. C 15, 7367 (1982).
[2] Y. Liao and M. S. Foster, Phys. Rev. Lett. 120, 236601 (2018).
[3] S. M. Davis and M. S. Foster, in preparation.