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String Order in Quench Dynamics as a Probe of Quantum Phase Transitions

  • H. P. Zhang
  • Z. Song
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Abstract

We study the anisotropic XY chain in a transverse field by introducing a global string order parameter and examining its equilibrium behavior and its quench dynamics from a fully polarized initial state. The corresponding string operator is defined as the product of local projected spin operators over the entire chain. The nonequilibrium order parameter is the long-time average of the logarithm of the string-operator expectation value per site after the quench. For the ground state, its field derivative is singular on the Ising critical lines; after the quench, the steady-state response also records the field boundaries and the anisotropy transition. We derive analytically the nonanalytic behavior of the order parameter at the quantum critical lines. Our results reveal a hidden nonlocal order underlying this paradigmatic model of conventional quantum phase transitions. They also connect measurable spin populations with equilibrium and dynamical topological structure.

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026string,
  title = {{String Order in Quench Dynamics as a Probe of Quantum Phase Transitions}},
  author = {H. P. Zhang and Z. Song},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30647},
  eprint = {2610.30647},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30647},
}
RIS
TY  - UNPB
TI  - String Order in Quench Dynamics as a Probe of Quantum Phase Transitions
AU  - H. P. Zhang
AU  - Z. Song
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.30647
UR  - https://arxiv.org/abs/2610.30647
AB  - We study the anisotropic XY chain in a transverse field by introducing a global string order parameter and examining its equilibrium behavior and its quench dynamics from a fully polarized initial state. The corresponding string operator is defined as the product of local projected spin operators over the entire chain. The nonequilibrium order parameter is the long-time average of the logarithm of the string-operator expectation value per site after the quench. For the ground state, its field derivative is singular on the Ising critical lines; after the quench, the steady-state response also records the field boundaries and the anisotropy transition. We derive analytically the nonanalytic behavior of the order parameter at the quantum critical lines. Our results reveal a hidden nonlocal order underlying this paradigmatic model of conventional quantum phase transitions. They also connect measurable spin populations with equilibrium and dynamical topological structure.
ER  -