2012/01/31 by Jutho Haegeman, David Pérez-Garcı́a, David Perez-Garcia +3 · 3 citations
Mathematics · Physics and Astronomy · #Bilinear interpolation #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Dimension (graph theory) #Gapless playback #Invariant (physics) #Mathematics #Order (exchange) #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum many-body systems #Quantum mechanics #Signature (topology) #Statistical physics #String (physics) #Symmetry (geometry) #Theoretical physics #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physrevlett.109.050402
published as Phys. Rev. Lett. 109, 050402 (2012) · 5 pages, 5 figures. v2: tiny corrections, accepted version, Journal-Ref added
openalex publication_date 2012/07/31 · arxiv created 2012/08/15 · arxiv updated 2012/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We introduce an order parameter for symmetry-protected phases in one dimension which allows us to directly identify those phases. The order parameter consists of stringlike 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.