Symmetry protection of topological phases in one-dimensional quantum spin systems
By Frank Pollmann, Erez Berg, Ari M. Turner, M. Oshikawa. 2009
579 citations recorded by the source corpus.
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 π rotations about the x, y, and z axes, (ii) time-reversal symmetry Sx,y,z→−Sx,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.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/9f89a693b6e39284276698e609fcb930cf8920d9
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In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
Citations in the corpus
- Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions (2017, background): “The even-integer-spin Haldane phases are trivial gapped states, just like the disordered product state of spin-0’s [13].”
- Average Symmetry-Protected Topological Phases (2022, unknown): “One way to characterize the clean cluster model is the nonlocal string order parameter in the ground-state [31, 72]:”
- Quantum spin liquid states (2016, background): “…the end states of integer spin chains are a manifestation of symmetry-protected topological (SPT) order (Chen et al., 2012; Gu and Wen, 2009; Pollmann et al., 2012), which manifests itself as a boundary action that 8 is protected by rotational (SO(3)) symmetry.1 For half-odd-integer spin…”
- Quantum Information Meets Quantum Matter (2015, background): “superconductors, and the theory of topological order became a theory with no experimental realization. However, the similarity [32] between chiral spin states and fractional quantum Hall (FQH) states [59,39] allows one to use the theory of topological order to describe different FQH states. FQH stat”