Kavli Affiliate: Shenghan Jiang
| Summary:
How do we detect topological phases from a single ground state? Entanglement entropy and spectrum have long been the standard tools — but the reduced density matrix (RDM) itself contains far more information. We show that the RDM of a 2D topologically ordered system, expressed at the entanglement cut, realizes a 1D mixed-state phase. For the $mathbbZ_2$ toric code phase, it is a 1D $mathbbZ_2$ strong-to-weak spontaneous symmetry breaking (SW-SSB) phase, where deconfinement of anyons manifests as the short-range correlation of both $mathbbZ_2$ charge and $mathbbZ_2$ domain-wall in the RDM. The bulk $e$-$m$ duality translates into a Kramers–Wannier self-duality of the SW-SSB phase. Extending the framework to gapped $mathbbZ_2$ spin liquids, the global spin-rotation symmetry manifests as an additional weak symmetry for the 1D RDM. Spin-$frac12$ spinons result in a cusp on the disorder parameter of spin-rotation at $θ=π$, providing a direct, ground-state signature of symmetry fractionalization. We verify this prediction analytically using the matrix product density operator formalism and numerically for the kagome-lattice resonating valence bond state. The proposed observable requires only a single ground-state wavefunction, making it amenable to quantum simulation platforms.
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