A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations

Abstract

We introduce exactly solvable models of interacting (Majorana) fermions in $d\ge 3$ spatial dimensions that realize a new kind of topological quantum order, building on a model presented in ref. [1]. These models have extensive topological ground-state degeneracy and a hierarchy of point-like, topological excitations that are only free to move within sub-manifolds 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.

13 pages, 5 figures

References in corpus (2)

• Local stabilizer codes in three dimensions without string logical operators
• Majorana Fermion Surface Code for Universal Quantum Computation

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