Home >  Conference > Gapless Kitaev Spin Liquid to Loop and String Gases through Tensor Networks

Gapless Kitaev Spin Liquid to Loop and String Gases through Tensor Networks

Date : Monday, June 10th, 2019 4:00 pm 〜 Place : Seminar Room 5 (A615), 6th Floor, ISSP Lecturer : Dr.Hyun-Yong Lee Affiliation : ISSP, The University of Tokyo Committee Chair : Naoki Kawashima (ext.63260)
e-mail: kawashima@issp.u-tokyo.ac.jp

Kitaev honeycomb model(KHM) is one of the rare examples of the exactly solvable quantum many-body model[1]. It hosts two distinct phases, the Z2 topologically ordered phase, which is adiabatically connected to the toric code state, and the gapless Kitaev spin liquid(KSL) phase exhibiting the low energy Majorana excitations[1]. In particular, the fact that the KSL phase can be driven into the non-Abelian topological phase by breaking the time-reversal symmetry attracts lots of interests in experimental and theoretical studies. In this talk, we try to understand the KSL from a new perspective, i.e., the loop gas(LG) and string gas(SG) states which are efficiently and compactly defined in the tensor network representation[2].
One can show in a local tensor level that the LG and SG states, which we propose, not only respect the symmetries of KSL but also satisfy the vortex-free condition[2]. Also, those are critical states characterized by Ising CFT and have the Z2 gauge redundancy which allows us to create and move the vortex excitations exactly. Furthermore, accurate variational energy for the KHM is obtained with only two variational parameters[2], which ensures that our ansatze represent quantitatively as well as qualitatively the KSL. We discuss their physical properties, relation to classical statistical mechanics and topological properties in details.

[1] A. Kitaev, Annals of Physics 321(2006) 2-111
[2] H.-Y. Lee, R. Kaneko, T. Okubo and N. Kawashima, arXiv:1901.05786


(Published on: Friday May 24th, 2019)