Symmetry defects and gauging for quantum states with matrix product unitary symmetries
- 1Max-Planck-Institut für Quantenoptik,Hans-Kopfermann-Str. 1, Garching, 85748, Germany
- 2Munich Center for Quantum Science and Technology, Schellingstraße 4, München, 80799, Germany
- 3University of Vienna, Faculty of Physics, Boltzmanngasse 5, 1090 Wien, Austria
Abstract
In this work, we examine the consequences of the existence of a finite group of matrix product unitary (MPU) symmetries for matrix product states (MPS). We generalize the well-understood picture of onsite unitary symmetries, which give rise to virtual symmetry defects given by insertions of operators in the bonds of the MPS. In the MPU case, we can define analogous defect tensors, this time sitting on lattice sites, that can be created, moved, and fused by local unitary operators. We leverage this formalism to study the gauging of MPU symmetries. We introduce a condition, block independence, under which we can gauge the symmetries by promoting the symmetry defects to gauge degrees of freedom, yielding an MPS of the same bond dimension that supports a local version of the symmetry given by commuting gauge constraints. Whenever block independence does not hold (which happens, in particular, whenever the symmetry representation is anomalous), a modification of our method which we call state-level gauging still gives rise to a locally symmetric MPS by promotion of the symmetry defects, at the expense of producing gauge constraints that do not commute on different sites.
Related
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BibTeX
@article{francorubio2026symmetry,
title = {{Symmetry defects and gauging for quantum states with matrix product unitary symmetries}},
author = {Adrián Franco-Rubio and Arkadiusz Bochniak and J. Ignacio Cirac},
journal = {Quantum},
year = {2026},
month = oct,
doi = {10.22331/q-2026-10-22-2243},
url = {https://quantum-journal.org/papers/q-2026-10-22-2243/},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Symmetry defects and gauging for quantum states with matrix product unitary symmetries
AU - Adrián Franco-Rubio
AU - Arkadiusz Bochniak
AU - J. Ignacio Cirac
PY - 2026
DA - 2026/10/22
JO - Quantum
DO - 10.22331/q-2026-10-22-2243
UR - https://quantum-journal.org/papers/q-2026-10-22-2243/
AB - In this work, we examine the consequences of the existence of a finite group of matrix product unitary (MPU) symmetries for matrix product states (MPS). We generalize the well-understood picture of onsite unitary symmetries, which give rise to virtual symmetry defects given by insertions of operators in the bonds of the MPS. In the MPU case, we can define analogous defect tensors, this time sitting on lattice sites, that can be created, moved, and fused by local unitary operators. We leverage this formalism to study the gauging of MPU symmetries. We introduce a condition, block independence, under which we can gauge the symmetries by promoting the symmetry defects to gauge degrees of freedom, yielding an MPS of the same bond dimension that supports a local version of the symmetry given by commuting gauge constraints. Whenever block independence does not hold (which happens, in particular, whenever the symmetry representation is anomalous), a modification of our method which we call state-level gauging still gives rise to a locally symmetric MPS by promotion of the symmetry defects, at the expense of producing gauge constraints that do not commute on different sites.
SN - 2521-327X
ER -