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Majorana Quantum Lego, a Route Towards Fracton Matter
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Fracton topological phases host fractionalized topological quasiparticles with restricted mobility, with promising applications to fault-tolerant quantum computation. While a variety of exactly solvable fracton models have been proposed, there is a need for platforms to realize them experimentally. We show that a rich set of fracton phases emerges in interacting Majorana band models whose building blocks are within experimental reach. Specifically, our Majorana constructions overcome a principal obstacle, namely the implementation of the complicated spin cluster interactions underlying fracton stabilizer codes. The basic building blocks of the proposed constructions include Coulomb blockaded Majorana islands and weak inter-island Majorana hybridizations. This setting produces a wide variety of fracton states and promises numerous opportunities for probing and controlling fracton phases experimentally. Our approach also reveals the relation between fracton phases and Majorana fermion codes and further generates a hierarchy of fracton spin liquids.
Forward citations
Cited by 4 Pith papers
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Electric Circuit Realizations of Fracton Physics
Networks of capacitors connected by ideal transformers conserve dipole moment, making electric charge immobile like fractons, with a linear steady-state charge profile.
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Constructing Quantum Spin Liquids Using Combinatorial Gauge Symmetry
A new 'combinatorial gauge symmetry' lets two-body spin Hamiltonians with Hadamard coupling matrices realize exact local Z2 gauge symmetries and, in a limit, topological spin liquids and the X-cube fracton model.
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Higher-order topological phase without crystalline symmetry
Subsystem symmetries can protect gapless hinges and corners in interacting 3D models, yielding higher-order topological phases that require no crystalline symmetry.
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Anisotropic layer construction of anisotropic fracton models
A coupled-layer construction from stacked 2D toric codes produces an exactly solvable anisotropic fracton model with lineon and planon excitations.
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