Does causal dynamics imply local interactions?

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Zoltán Zimborás
  • Terry Farrelly
  • Szilárd Farkas
  • Lluis Masanes

Research Organisations

External Research Organisations

  • Hungarian Academy of Sciences
  • Budapest University of Technology and Economics
  • University of Queensland
  • University College London (UCL)
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Details

Original languageEnglish
Number of pages9
JournalQuantum
Volume6
Publication statusPublished - 2022

Abstract

We consider quantum systems with causal dynamics in discrete spacetimes, also known as quantum cellular automata (QCA). Due to time-discreteness this type of dynamics is not characterized by a Hamiltonian but by a one-time-step unitary. This can be written as the exponential of a Hamiltonian but in a highly non-unique way. We ask if any of the Hamiltonians generating a QCA unitary is local in some sense, and we obtain two very different answers. On one hand, we present an example of QCA for which all generating Hamiltonians are fully non-local, in the sense that interactions do not decay with the distance. We expect this result to have relevant consequences for the classification of topological phases in Floquet systems, given that this relies on the effective Hamiltonian. On the other hand, we show that all one-dimensional quasi-free fermionic QCAs have quasi-local generating Hamiltonians, with interactions decaying exponentially in the massive case and algebraically in the critical case. We also prove that some integrable systems do not have local, quasi-local nor low-weight constants of motion; a result that challenges the standard definition of integrability.

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Cite this

Does causal dynamics imply local interactions? / Zimborás, Zoltán; Farrelly, Terry; Farkas, Szilárd et al.
In: Quantum, Vol. 6, 2022.

Research output: Contribution to journal › Article › Research › peer review

Zimborás Z, Farrelly T, Farkas S, Masanes L. Does causal dynamics imply local interactions? Quantum. 2022;6. doi: 10.48550/arXiv.2006.10707, 10.22331/Q-2022-06-29-748
Zimborás, Zoltán ; Farrelly, Terry ; Farkas, Szilárd et al. / Does causal dynamics imply local interactions?. In: Quantum. 2022 ; Vol. 6.
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title = "Does causal dynamics imply local interactions?",
abstract = "We consider quantum systems with causal dynamics in discrete spacetimes, also known as quantum cellular automata (QCA). Due to time-discreteness this type of dynamics is not characterized by a Hamiltonian but by a one-time-step unitary. This can be written as the exponential of a Hamiltonian but in a highly non-unique way. We ask if any of the Hamiltonians generating a QCA unitary is local in some sense, and we obtain two very different answers. On one hand, we present an example of QCA for which all generating Hamiltonians are fully non-local, in the sense that interactions do not decay with the distance. We expect this result to have relevant consequences for the classification of topological phases in Floquet systems, given that this relies on the effective Hamiltonian. On the other hand, we show that all one-dimensional quasi-free fermionic QCAs have quasi-local generating Hamiltonians, with interactions decaying exponentially in the massive case and algebraically in the critical case. We also prove that some integrable systems do not have local, quasi-local nor low-weight constants of motion; a result that challenges the standard definition of integrability.",
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note = "Funding Information: The authors would like to thank Tobias J. Osborne for useful discussions. LM acknowledges financial support by the UK{\textquoteright}s Engineering and Physical Sciences Research Council (grant number EP/R012393/1). TF was supported by the ERC grants QFTCMPS and SIQS, the cluster of excellence EXC201 Quantum Engineering and Space-Time Research, the DFG through SFB 1227 (DQ-mat), and the Australian Research Council Centres of Excellence for Engineered Quantum Systems (EQUS, CE170100009). ZZ acknowledges support from the J{\'a}nos Bolyai Research Scholarship, the UKNP Bolyai+ Grant, and the NKFIH Grants No. K124152, K124176 KH129601, K120569, and from the Hungarian Quantum Technology National Excellence Program, Project No. 2017-1.2.1-NKP-2017-00001. ",
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AU - Zimborás, Zoltán

AU - Farrelly, Terry

AU - Farkas, Szilárd

AU - Masanes, Lluis

N1 - Funding Information: The authors would like to thank Tobias J. Osborne for useful discussions. LM acknowledges financial support by the UK’s Engineering and Physical Sciences Research Council (grant number EP/R012393/1). TF was supported by the ERC grants QFTCMPS and SIQS, the cluster of excellence EXC201 Quantum Engineering and Space-Time Research, the DFG through SFB 1227 (DQ-mat), and the Australian Research Council Centres of Excellence for Engineered Quantum Systems (EQUS, CE170100009). ZZ acknowledges support from the János Bolyai Research Scholarship, the UKNP Bolyai+ Grant, and the NKFIH Grants No. K124152, K124176 KH129601, K120569, and from the Hungarian Quantum Technology National Excellence Program, Project No. 2017-1.2.1-NKP-2017-00001.

PY - 2022

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