Haegeman, Jutho and Pérez-García, David and Cirac, Ignacio and Schuch, Norbert (2012) Order Parameter for Symmetry-Protected Phases in One Dimension. Physical Review Letters, 109 (5). Art. No. 050402. ISSN 0031-9007. doi:10.1103/PhysRevLett.109.050402. https://resolver.caltech.edu/CaltechAUTHORS:20120910-113643342
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Abstract
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.
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| Additional Information: | © 2012 American Physical Society. Received 2 April 2012; published 31 July 2012. We thank J. de Boer and F. Verstraete for helpful comments. Parts of this work were carried out at the Perimeter Institute in Waterloo, Canada, and the Centro de Ciencias Pedro Pascual in Benasque, Spain. This work has been supported by the Alexander von Humboldt Foundation, the Caltech Institute for Quantum Information and Matter (an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation), the NSF Grant No. PHY-0803371, the EU grants QUEVADIS and QUERG, the Spanish projects QUITEMAD and MTM2011-26912, the FWF SFB grants FoQuS and ViCoM, and the DFG-Forschergruppe 635. | ||||||||||||||||||||||||
| Group: | Institute for Quantum Information and Matter | ||||||||||||||||||||||||
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| Issue or Number: | 5 | ||||||||||||||||||||||||
| Classification Code: | PACS: 05.30.d; 03.65.Vf; 75.10.Pq | ||||||||||||||||||||||||
| DOI: | 10.1103/PhysRevLett.109.050402 | ||||||||||||||||||||||||
| Record Number: | CaltechAUTHORS:20120910-113643342 | ||||||||||||||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20120910-113643342 | ||||||||||||||||||||||||
| Official Citation: | Haegeman, J., D. Pérez-García, et al. (2012). "Order Parameter for Symmetry-Protected Phases in One Dimension." Physical Review Letters 109(5): 050402. | ||||||||||||||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||||||||||||||
| ID Code: | 33963 | ||||||||||||||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||||||||||||||
| Deposited By: | INVALID USER | ||||||||||||||||||||||||
| Deposited On: | 11 Sep 2012 20:26 | ||||||||||||||||||||||||
| Last Modified: | 09 Nov 2021 23:05 |
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