Twin condensable algebras are introduced as condensable algebras with identical anyon decompositions but inequivalent algebra structures, yielding distinct symmetric phases in group-theoretical topological orders.
An order parameter for symmetry-protected phases in one dimension
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abstract
We introduce an order parameter for symmetry-protected phases in one dimension which allows to directly identify those phases. The order parameter consists of string-like operators and swaps, but differs from conventional string order operators in that it only depends on the symmetry but not on the state. We verify our framework through numerical simulations for the SO(3) invariant spin-1 bilinear-biquadratic model which exhibits a dimerized and a Haldane phase, and find that the order parameter not only works very well for the dimerized and the Haldane phase, but it also returns a distinct signature for gapless phases. Finally, we discuss possible ways to measure the order parameter in experiments with cold atoms.
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cond-mat.str-el 1years
2026 1verdicts
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Twin Algebras: Condensable Algebras beyond Anyons
Twin condensable algebras are introduced as condensable algebras with identical anyon decompositions but inequivalent algebra structures, yielding distinct symmetric phases in group-theoretical topological orders.