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Non-invertible symmetries act locally by quantum operations
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Non-invertible symmetries of quantum field theories and many-body systems generalize the concept of symmetries by allowing non-invertible operations in addition to more ordinary invertible ones described by groups. The aim of this paper is to point out that these non-invertible symmetries act on local operators by quantum operations, i.e. completely positive maps between density matrices, which form a natural class of operations containing both unitary evolutions and measurements and play an important role in quantum information theory. This observation will be illustrated by the Kramers--Wannier duality of the one-dimensional quantum Ising chain, which is a prototypical example of non-invertible symmetry operations.
Forward citations
Cited by 2 Pith papers
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Distinct finite-temperature phase diagrams of non-invertible Kennedy--Tasaki duals
In three dimensions, a cluster-model interpolation and its non-invertible Kennedy–Tasaki dual have inequivalent finite-T phase diagrams over a finite window of the interpolation, proven exactly at s=0 and mapped by QMC.
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Systematic Construction of Kramers-Wannier-like Dualities in Quantum Lattice Models from Integrability
Lax matrices built from a fermionic R-matrix yield a family of lattice Hamiltonians with explicitly constructed non-invertible Kramers-Wannier-like symmetry operators and spectrum-preserving dualities.
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