Detection of symmetry-protected topological phases in one dimension
By Frank Pollmann, Ari M. Turner. 2012
278 citations recorded by the source corpus.
A topological phase is a phase of matter which cannot be characterized by a local order parameter. It has been shown that gapped symmetric phases in one-dimensional (1D) systems can be completely characterized using tools related to projective representations of the symmetry groups. We explain two ways to detect these symmetry protected topological phases in 1D. First, we give a numerical approach for directly extracting the projective representations from a matrix-product state representation. Second, we derive nonlocal order parameters for time-reversal and inversion symmetry, and discuss a generalized string order for local symmetries for which the regular string-order parameter cannot be applied. We furthermore point out that the nonlocal order parameter for these topological phases is actually related to topological surfaces.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/37eb19864946789db97bfccedd563d7279f193e5
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In Atomic and Molecular Physics, and Optics
- Ashvin Vishwanath
- Norbert Schuch
- Frank Verstraete
- R. Verresen
- I. Cirac
- Peter Zoller
- Hsin-Yuan Huang
- Frank Pollmann
In Condensed Matter Physics
- Frank Verstraete
- Norbert Schuch
- Ryan Thorngren
- I. Cirac
- Frank Pollmann
- Ashvin Vishwanath
- R. Verresen
- David Pérez-García
Citations in the corpus
- The randomized measurement toolbox (2022, background): “These invariants are highly non-local and/or nonlinear correlators of the many-body wavefunction that unambiguously identify SPT phases 59 .”
- Provably efficient machine learning for quantum many-body problems (2021, background): “The system’s three distinct phases are characterized by the many-body topological invariant ~ ZR, discussed in (62, 87).”
- Long-Range Entanglement from Measuring Symmetry-Protected Topological Phases (2021, background): “Indeed, the very reason the string order parameters have nontrivial end-point operators is because they are able to cancel out the virtual V g action of the symmetry string or disorder operator [117].”
- Gapless Topological Phases and Symmetry-Enriched Quantum Criticality (2019, background): “Nevertheless, in practice knowing the charges is often equivalent to knowing the projective representations (the simplest known counter-example involves a group of 128 elements [49]).”
- Matrix product states and projected entangled pair states: Concepts, symmetries, theorems (2020, methodology): “As the group is Abelian, ω(h.g, h−1) = −ω(g, h), and hence the expectation value does not have to vanish if α(h) = ω(g, h) − ω(h, g).”