A new kind of topological quantum order: A dimensional hierarchy of quasiparticles built from stationary excitations
Name
PhysRevB.92.235136.pdf
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1.47 MB
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085d5c5806442d0b6a6aaf5f7aed9186
Author(s)
Haah, Jeongwan
Fu, Liang
Vijay, Ksheerasagar
Date Issued
December 2015
Journal
Physical Review B
Publisher
American Physical Society
Citation
Vijay, Sagar, Jeongwan Haah, and Liang Fu. “A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations.” Physical Review B 92, no. 23 (December 21, 2015). © 2015 American Physical Society
Version
Final published version
Abstract
We introduce exactly solvable models of interacting (Majorana) fermions in d≥3 spatial dimensions that realize a new kind of fermion topological quantum order, building on a model presented by S. Vijay, T. H. Hsieh, and L. Fu [Phys. Rev. X 5, 041038 (2015)10.1103/PhysRevX.5.041038]. These models have extensive topological ground-state degeneracy and a hierarchy of pointlike, topological excitations that are only free to move within submanifolds of the lattice. In particular, one of our models has fundamental excitations that are completely stationary. To demonstrate these results, we introduce a powerful polynomial representation of commuting Majorana Hamiltonians. Remarkably, the physical properties of the topologically ordered state are encoded in an algebraic variety, defined by the common zeros of a set of polynomials over a finite field. This provides a “geometric” framework for the emergence of topological order.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.92.235136
