The DOI matches its Crossref record; 31 of the 31 references it cites were found in a registry or an index.
Symmetry protection of topological phases in one-dimensional quantum spin systems
Open accessAbstract
We discuss the characterization and stability of the Haldane phase in integer spin chains on the basis of simple, physical arguments. We find that an odd-$S$ Haldane phase is a topologically nontrivial phase which is protected by any one of the following three global symmetries: (i) the dihedral group of $\ensuremath{\pi}$ rotations about the $x$, $y$, and $z$ axes, (ii) time-reversal symmetry ${S}^{x,y,z}\ensuremath{\rightarrow}\ensuremath{-}{S}^{x,y,z}$, and (iii) link inversion symmetry (reflection about a bond center), consistent with previous results [Phys. Rev. B 81, 064439 (2010)]. On the other hand, an even-$S$ Haldane phase is not topologically protected (i.e., it is indistinct from a trivial, site-factorizable phase). We show some numerical evidence that supports these claims, using concrete examples.
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Cites
Z 2 Topological Order and the Quantum Spin Hall Effect
Kane, C. L., & Mele, E. J. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.146802 · Cited by 6,460
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Entanglement Entropy and Quantum Field Theory
Calabrese, P., & Cardy, J. (2004) · arXiv · doi:10.48550/arxiv.hep-th/0405152 · Cited by 3,275
Entanglement entropy and quantum field theory
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Rigorous results on valence-bond ground states in antiferromagnets
Affleck, I., Kennedy, T., Lieb, E. H., & Tasaki, H. (1987) · Physical Review Letters · doi:10.1103/physrevlett.59.799 · Cited by 2,223
Surprises on the Way from One- to Two-Dimensional Quantum Magnets: The Ladder Materials
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Entanglement spectrum of a topological phase in one dimension
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Self-citation
Cited by
Classification of topological quantum matter with symmetries
Chiu, C.-K., Teo, J. C. Y., Schnyder, A. P., & Ryu, S. (2016) · Reviews of Modern Physics · doi:10.1103/revmodphys.88.035005 · Cited by 2,736
Zeng, M., Xiao, Y., Liu, J., Yang, K., & Fu, L. (2018) · Chemical Reviews · doi:10.1021/acs.chemrev.7b00633 · Cited by 574
Majorana Fermions and Topology in Superconductors
Sato, M., & Fujimoto, S. (2016) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.85.072001 · Cited by 373
Prethermal Phases of Matter Protected by Time-Translation Symmetry
Else, D. V., Bauer, B., & Nayak, C. (2017) · Physical Review X · doi:10.1103/physrevx.7.011026 · Cited by 283
Topological surface states in nodal superconductors
Schnyder, A. P., & Brydon, P. M. R. (2015) · Journal of Physics: Condensed Matter · doi:10.1088/0953-8984/27/24/243201 · Cited by 176
Metadata
- Authors
- Pollmann, F., Berg, E., Turner, A. M., & Oshikawa, M.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2012-02-22
- Volume
- 85
- Issue
- 7
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W2008822316
- Cited by
- 848
- References
- 31
- FWCI
- 22.27
- Type
- journal article
- Language
- en
- Open access
- bronze
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