Crossover of Correlation Functions near a Quantum Impurity in a Tomonaga-Luttinger Liquid
Chung-Yu Lo1, Yoshiki Fukusumi3, Masaki Oshikawa3, Ying-Jer Kao2, Pochung Chen1*
1Department of Physics, National Tsing Hua University, Hsinchu, Taiwan
2Department of Physics, National Taiwan University, Taipei, Taiwan
3Institute for Solid State Physics, University of Tokyo, Kashiwa, Japan
* Presenter:Pochung Chen,
An impurity in a Tomonaga-Luttinger liquid leads to a crossover
between short- and long-distance regime which describes many physical
phenomena. However, calculation of the entire crossover of
correlation functions over different length scales has been difficult.
We develop a powerful numerical method based on infinite DMRG.
By utilizing infinite boundary conditions we can obtain correlation functions
within a finite-size window that contains the impurity.
For the $S=1/2$ chain, we demonstrate that the full crossover
can be precisely obtained, and that their limiting behaviors
show a good agreement with field-theory predictions.

Keywords: quantum impurity, Tomonaga-Luttinger Liquid, infinite boundary condition, infinite DMRG, crossover phenomena