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PreprintCC BY 4.0arXiv

Spread Complexity for Local Operator Quenches with Conserved Momentum

  • Ali Fatemiabhari
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Abstract

We study a family of locally excited states in two-dimensional conformal field theories in different setups, defined on the plane, on the cylinder, or at finite temperature. These states are constructed by assigning independent chiral and anti-chiral regulators to a local primary operator, leading to excitations carrying net momentum. We analytically calculate the first few Lanczos coefficients and the early time behaviour of the spread complexity associated with these states. Then, using numerical methods, we obtain the coefficients reaching larger Krylov indices and find the associated spread complexity for a longer range of time evolution. We also compare the rate of change of the resulting spread complexity with the proposed holographic dual quantity, related to the proper momentum of an infalling particle in the dual bulk, but we observe a mismatch.

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Cite

BibTeXRIS
BibTeX
@misc{fatemiabhari2026spread,
  title = {{Spread Complexity for Local Operator Quenches with Conserved Momentum}},
  author = {Ali Fatemiabhari},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.31867},
  eprint = {2609.31867},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31867},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Spread Complexity for Local Operator Quenches with Conserved Momentum
AU  - Ali Fatemiabhari
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.31867
UR  - https://arxiv.org/abs/2609.31867
AB  - We study a family of locally excited states in two-dimensional conformal field theories in different setups, defined on the plane, on the cylinder, or at finite temperature. These states are constructed by assigning independent chiral and anti-chiral regulators to a local primary operator, leading to excitations carrying net momentum. We analytically calculate the first few Lanczos coefficients and the early time behaviour of the spread complexity associated with these states. Then, using numerical methods, we obtain the coefficients reaching larger Krylov indices and find the associated spread complexity for a longer range of time evolution. We also compare the rate of change of the resulting spread complexity with the proposed holographic dual quantity, related to the proper momentum of an infalling particle in the dual bulk, but we observe a mismatch.
ER  -