Counting statistics in interacting one-dimensional conductors

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 in zero temperature case leads to a) violation of the moment generating function's periodicity along the counting field b) matrix size cutoff in the logarithmic divergent terms. The periodicity can be restored using the Fisher-Hartwig conjecture, as was shown for non-interacting one-dimensional electrons [2,3]. Here, we aim to go beyond and include interactions. For weak interactions we developed a modification of the Matsubara diagrammatic approach, which allows us an 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, moreover, we are able to determine quantitively the infrared cutoff in noise terms as well as its dependence on parameter K. We also found a surprising counterpart of the charge-density wave effect in the cumulant generating function.