A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations
By S. Vijay, Jeongwan Haah, Liang Fu. 2015
315 citations recorded by the source corpus.
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.
Subfields: Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/9cc35b9d62a9237154251290f796ae9d60e966e6
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In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Localization in Fractonic Random Circuits (2018, background): “[29] Sagar Vijay, Jeongwan Haah, and Liang Fu, “A new kind of topological quantum order: A dimensional hierarchy of quasiparticles built from stationary excita-”
- Generalized Electromagnetism of Subdimensional Particles: A Spin Liquid Story (2016, background): “es of subdimensional particles are also possible. This subdimensional behavior makes these theories the natural U(1) analogues of the discrete \fracton" models constructed by Vijay, Haah, and Fu [6, 7, 8]. These phases also exhibit an emergent sort of electromagnetism, but of a more exotic form”
- Localization from Hilbert space shattering: From theory to physical realizations (2020, background): “Most of this work will focus on models inspired by fracton systems [28–34] in which excitations are known to exhibit restricted mobility.”
- Fracton Topological Order, Generalized Lattice Gauge Theory and Duality (2016, methodology): “Thus far, two broad classes of fracton topological orders have been found: Type I fracton phases, such as the Chamon-BravyiLeemhuis-Terhal (CBLT) model [14,15] and the Majorana cubic model [18], have fracton excitations appearing at the corners of membrane operators; composites of fractons form topo”
- Fractons (2018, background): “[11] Sagar Vijay, Jeongwan Haah, and Liang Fu, “A new kind of topological quantum order: A dimensional hierarchy of quasiparticles built from stationary excitations,” Phys.”
- Fracton hydrodynamics (2020, background): “First discovered in exactly solvable lattice models [13–15], fracton phases are now at the frontier of multiple areas of theoretical physics.”
- Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians (2019, background): “Constrained dynamics occurs naturally in so-called fracton systems, which are characterized by the existence of excitations that exhibit restricted mobility [47, 48].”
- Towards Classification of Fracton Phases: The Multipole Algebra (2018, background): “Various combinations of fractons can freely move around on lower-dimensional submanifolds [6,7].”
- Fracton phases of matter (2020, methodology): “[3] Sagar Vijay, Jeongwan Haah, and Liang Fu, “A new kind of topological quantum order: A dimensional hierarchy of quasiparticles built from stationary excitations,” Phys.”