No-go theorems for dual Hamiltonians of Non-Abelian Lattice Gauge Theories
Abstract
Hamiltonian simulations of lattice gauge theories promise new insights into the inner workings of QCD. The rapid development of quantum computing hardware suggests that large scale simulations may soon become feasible. However, no efficient formulation suitable for simulations near the continuum limit is currently known for the non-Abelian case, and existing candidates typically feature long range interactions in the electric part of the Hamiltonian. We prove that such non- localities are unavoidable when the gauge configuration is reparametrised while preserving both the number of degrees of freedom and the fundamental commutation relations. We then attempt to mitigate this by introducing additional gauge links alongside additional constraints. Although this approach is successful in U(1), we prove that the corresponding construction is inconsistent for non-Abelian lattice gauge theories.
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BibTeX
@misc{garofalo2026nogo,
title = {{No-go theorems for dual Hamiltonians of Non-Abelian Lattice Gauge Theories}},
author = {Marco Garofalo and Tobias Hartung and Timo Jakobs and Paul Ludwig and Johann Ostmeyer and Carsten Urbach},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39780},
eprint = {2609.39780},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39780},
}
RIS
TY - UNPB
TI - No-go theorems for dual Hamiltonians of Non-Abelian Lattice Gauge Theories
AU - Marco Garofalo
AU - Tobias Hartung
AU - Timo Jakobs
AU - Paul Ludwig
AU - Johann Ostmeyer
AU - Carsten Urbach
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39780
UR - https://arxiv.org/abs/2609.39780
AB - Hamiltonian simulations of lattice gauge theories promise new insights into the inner workings of QCD. The rapid development of quantum computing hardware suggests that large scale simulations may soon become feasible. However, no efficient formulation suitable for simulations near the continuum limit is currently known for the non-Abelian case, and existing candidates typically feature long range interactions in the electric part of the Hamiltonian. We prove that such non- localities are unavoidable when the gauge configuration is reparametrised while preserving both the number of degrees of freedom and the fundamental commutation relations. We then attempt to mitigate this by introducing additional gauge links alongside additional constraints. Although this approach is successful in U(1), we prove that the corresponding construction is inconsistent for non-Abelian lattice gauge theories.
ER -