Regensburg 2022 – scientific programme
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TT: Fachverband Tiefe Temperaturen
TT 34: Correlated Electrons: Theory 2
TT 34.3: Talk
Thursday, September 8, 2022, 15:30–15:45, H23
Counting statistics in interacting one-dimensional conductors — •Oleksiy Kashuba1, Roman Riwar1, Fabian Hassler2, and Thomas Schmidt3 — 1Forschungszentrum Jülich — 2RWTH Aachen — 3Luxemburg Uni
The calculation of the cumulant generating function of a given observable, such as the charge, is nontrivial even for the non-interacting systems. This problem is closely connected to the problem of Toeplitz eigenvalues and the Szego-Kac theorem [1]. The application of the latter leads to a violation of the moment generating function’s periodicity along the counting field. This periodicity can be restored using the Fisher-Hartwig conjecture, as was shown for non-interacting one-dimensional electrons [2]. Here, we aim to go beyond and include interactions. For weak interactions, a modification of the Matsubara diagrammatic approach was developed, allowing us explicit calculation of the interaction corrections to the cumulant generating function. All obtained terms preserve the periodic constraint of the moment generating function. The obtained result is in a good agreement at low filling with the noise suppression in Luttinger liquid for K<1. We also found a surprising counterpart of the charge-density wave effect in the cumulant generating function.
[1] Basor, Morrison, Linear Algebra and its Appl. 202 (1994), 129
[2] Aristov, Phys. Rev. B 57 (1998), 12825