Orthogonality catastrophe and quantum speed limit for spin chain at finite temperature

Zheng-Rong Zhu; Qing Wang; Jian Zou; Bin Shao; Lian-Ao Wu

doi:10.1038/s41598-022-09010-5

Orthogonality catastrophe and quantum speed limit for spin chain at finite temperature

Sci Rep. 2022 Mar 23;12(1):5058. doi: 10.1038/s41598-022-09010-5.

Authors

Zheng-Rong Zhu^{1

2}, Qing Wang^{1

2}, Jian Zou¹, Bin Shao^{3

4}, Lian-Ao Wu^{5

6}

Affiliations

¹ School of Physics, Beijing Institute of Technology, Beijing, 100081, China.
² Yangtze Delta Region Academy of Beijing Institute of Technology, Jiaxing, 314019, China.
³ School of Physics, Beijing Institute of Technology, Beijing, 100081, China. sbin610@bit.edu.cn.
⁴ Yangtze Delta Region Academy of Beijing Institute of Technology, Jiaxing, 314019, China. sbin610@bit.edu.cn.
⁵ Ikerbasque, Basque Foundation for Science, 48011, Bilbao, Spain.
⁶ Department of Physics, The Basque Country University (EHU/UPV), PO Box 644, 48080, Bilbao, Spain.

Abstract

We present an interesting relationship between the orthogonality catastrophe (OC) and the quantum speed limit (QSL) for a spin chain with uniform nearest neighbour couplings perturbed by an impurity spin. We thoroughly study the catastrophic QSL that specifies a bound on the evolution time between the initial and final states and in this respect, link it to the emerging OC effect. It is found that the speed of state evolution subtle but fundamental, and the bound characterized by QSL shows the same behaviours as the OC effect in the thermodynamic limit. It allows us to reveal some universal properties, in particular finite temperature effects. Significantly, the threshold of temperature and system size is clearly demonstrated for the QSL under finite temperature.