We have developed a continuous-time quantum Monte Carlo method for one-dimensional quantum impurity systems [1], where the one-dimensional bulk part is described by the Tomonaga-Luttinger liquid. The method is applied to back-scattering potential problem in a spinless quantum wire [2], and XXZ Kondo problem in a helical liquid [3]. Absence of the negative sign problem in this approach to these systems allows us to calculate accurate physical quantities at very low temperatures. We will also discuss the single-electron Green’s function (or local density of states) in the presence of a two-particle backward scattering impurity [3] in a helical liquid and possible application of the present method to the topological Kondo systems [4].

Reference:
[1] K. Hattori and A. Rosch, Phys. Rev. B 90, 115103 (2014).
[2] C. L. Kane and M. P. A. Fisher, Phys. Rev. Lett. 68, 1220 (1992).
[3] C. Wu, B. A. Bernevig, and S. C. Zhang, Phys. Rev. Lett. 96, 106401 (2006).
[4] B. Beri and N. R. Cooper, Phys. Rev. Lett. 109, 156803 (2012).