Dynamical zero modes and boundary dependence in dynamical quantum phase transitions

@misc{lin2026dynamical,
  title = {{Dynamical zero modes and boundary dependence in dynamical quantum phase transitions}},
  author = {Siyan Lin and Xu Feng and Xiuhua Tian and Shu Chen},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2607.03438},
  eprint = {2607.03438},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.03438},
}

TY  - UNPB
TI  - Dynamical zero modes and boundary dependence in dynamical quantum phase transitions
AU  - Siyan Lin
AU  - Xu Feng
AU  - Xiuhua Tian
AU  - Shu Chen
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2607.03438
UR  - https://arxiv.org/abs/2607.03438
AB  - Boundary conditions are usually expected to cause only finite-size corrections to bulk quantities, but this expectation can fail for dynamical quantum phase transitions. In this work, we show that such boundary dependence is encoded in dynamical zero modes (DZMs) of the Loschmidt matrix, which are defined as singular vectors whose singular values vanish in the thermodynamic limit. Using the Su-Schrieffer-Heeger (SSH), extended SSH, and Kitaev models as examples, we find that the time interval where the Loschmidt rate functions (LRFs) under periodic and open boundary conditions differ coincides with the emergence of DZMs in the open-boundary Loschmidt matrix. These modes carry the boundary-dependent contribution: removing them from the open-boundary LRF recovers the periodic-boundary result. We further show that these DZMs lead to finite-precision numerical instability, since their finite-size singular values decay exponentially with system size and eventually become unresolved in fixed-precision arithmetic. A reliable small-size branch before this loss of precision can be used to estimate the LRF in the thermodynamic limit by linear extrapolation. Our results identify DZMs as both a diagnostic of boundary-dependent LRFs and the origin of the associated numerical instability.
ER  -