Crossover of Correlation Functions near a Quantum Impurity in a Tomonaga-Luttinger Liquid

Chung-Yu Lo¹, Yoshiki Fukusumi³, Masaki Oshikawa³, Ying-Jer Kao², Pochung Chen^1*

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, email:pcchen@phys.nthu.edu.tw

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