Abstract
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.
Highlights
Searching for and exploring exotic phases of matter is a principal goal of condensed matter physics
In the presence of strong interactions, quantum many-body systems composed of a limited number of elementary particles assume a remarkable variety of exotic phases whose low-energy degrees of freedom are much richer than suggested by their constituents
The low-energy properties of these topologically ordered states are characterized by topological quantum field theories (TQFTs) [3,4]
Summary
Searching for and exploring exotic phases of matter is a principal goal of condensed matter physics. In the presence of strong interactions, quantum many-body systems composed of a limited number of elementary particles assume a remarkable variety of exotic phases whose low-energy degrees of freedom are much richer than suggested by their constituents Prominent examples of such emergent quantum phases are topological phases, whose quasiparticle excitations carry fractional quantum numbers and obey anyonic statistics [1,2]. This raises the question whether and how such exotic fracton states emerge in models with more physical ingredients and interactions These might be amenable to experimental implementation and, assuming tunable interaction parameters, allow for controlling and manipulating fracton phases and excitations, e.g., for quantum computing. Our Majorana-based setups for fracton models imply that fractonic phases of matter can emerge from strongly interacting one-dimensional p-wave superconductors. The Hamiltonian can be tuned away from the stabilizer limit to explore confinement and disorder effects on fracton matter
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