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Detection of 2D SPT Order with Partial Symmetries
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A method of using partial symmetries to distinguish two dimensional symmetry protected topological (SPT) phases of on-site, unitary symmetries is proposed. This novel order parameter takes a wavefunction, such as a ground state of a lattice model, and detects its SPT invariants as expectation values of finitely supported operators, without the need for flux insertion. The construction exploits the rotational symmetry of the lattice to extract on-site SPT invariants, building upon prior work on probing crystalline SPT phases with partial rotations. The method is demonstrated by computing the order parameter analytically on group cohomology models and numerically on a family of states interpolating between the CZX state and a trivial state. Its robustness is suggested by interpreting partial symmetries as generating the topological partition functions of lens spaces.
Forward citations
Cited by 2 Pith papers
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Detection of 2D SPT phases under decoherence
A partial-symmetry order parameter, J_{g,h,M}, is shown to extract the SPT invariants of two-dimensional mixed states protected jointly by strong and weak symmetries in CZX-type models.
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Diagnosing 2D symmetry protected topological states via mixed state anomaly
The RDM of a 2D Z2 SPT state acts as a 1D anomalous mixed state whose twisted disorder parameter contains a quantized topological constant (D=4 with time reversal) and supports symmetry-breaking-type long-range order.
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