Topological Phases of One-Dimensional Fermions: An Entanglement Point of View
By Ari M. Turner, Frank Pollmann, Erez Berg. 2010
344 citations recorded by the source corpus.
The effect of interactions on topological insulators and superconductors remains, to a large extent, an open problem. Here, we describe a framework for classifying phases of one-dimensional interacting fermions, focusing on spinless fermions with time-reversal symmetry and particle number parity conservation, using concepts of entanglement. In agreement with an example presented by L. Fidkowski and A. Kitaev [Phys. Rev. B 81, 134509 (2010)], we find that in the presence of interactions there are only eight distinct phases which obey a ${\mathbb{Z}}_{8}$ group structure. This is in contrast to the $\mathbb{Z}$ classification in the noninteracting case. Each of these eight phases is characterized by a unique set of bulk invariants, related to the transformation laws of its entanglement (Schmidt) eigenstates under symmetry operations, and has a characteristic degeneracy of its entanglement levels. If translational symmetry is present, the number of distinct phases increases to 16.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/f899df9f9fc7e9ddf088f603daf1f7ab3b999c5d
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In Atomic and Molecular Physics, and Optics
- Ashvin Vishwanath
- Ryan Thorngren
- T. Senthil
- Thomas Hartman
- R. Verresen
- Wladimir A. Benalcazar
- Mark Van Raamsdonk
- T. Hughes
In Condensed Matter Physics
- Ashvin Vishwanath
- Ryan Thorngren
- T. Senthil
- R. Verresen
- T. Faulkner
- Nathanan Tantivasadakarn
- T. Hughes
- N. G. Jones
Citations in the corpus
- Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect (2012, background): “In these phases, the bulk appears to local probes as a rather conventional gapped state.”
- Gravitation from entanglement in holographic CFTs (2013, background): “This was motivated in part by the importance of quantum entanglement for understanding quantum phases of matter in condensed matter systems [6].”
- Long-Range Entanglement from Measuring Symmetry-Protected Topological Phases (2021, methodology): “This can be derived using the notion of symmetry fractionalization [24].”