Majorana Quantum Lego, a Route Towards Fracton Matter

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.

References in corpus (8)

• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Local stabilizer codes in three dimensions without string logical operators
• Topological Quantum Distillation
• Majorana box qubits
• Fracton topological phases from strongly coupled spin chains
• Correlation function diagnostics for type-I fracton phases
• Arbitrary Dimensional Majorana Dualities and Network Architectures for Topological Matter
• Finite-Temperature Screening of U(1) Fractons

Cited by in corpus (26)

• Fracton Phases of Matter
• Anomalous Diffusion in Dipole- and Higher-Moment Conserving Systems
• Foliated Quantum Field Theory of Fracton Order
• Rank-2 $U(1)$ spin liquid on the breathing pyrochlore lattice
• Crystal-to-Fracton Tensor Gauge Theory Dualities
• Fractonic Chern-Simons and BF theories
• Gauging fractons: immobile non-Abelian quasiparticles, fractals, and position-dependent degeneracies
• Anisotropic layer construction of anisotropic fracton models
• Fractons from polarons
• Construction of Fractal Order and Phase Transition with Rydberg Atoms
• Subband occupation in semiconductor-superconductor nanowires
• Constructing Quantum Spin Liquids Using Combinatorial Gauge Symmetry
• Quantum robustness of fracton phases
• Optimal Thresholds for Fracton Codes and Random Spin Models with Subsystem Symmetry
• Foliated BF theories and Multipole symmetries
• Hyperbolic Fracton Model, Subsystem Symmetry, and Holography II: The Dual Eight-Vertex Model
• Lieb-Schultz-Mattis type constraints on Fractonic Matter
• Tearing Fractons
• Scalar, fermionic and supersymmetric field theories with subsystem symmetries in d+1 dimensions
• Electric Circuit Realizations of Fracton Physics
• Fragile spin liquid in three dimensions
• Irrational moments and signatures of higher-rank gauge theories in diluted classical spin liquids
• Critical region of topological trivial and nontrivial phases in interacting Kitaev chain with spatially varying potentials
• Sub-symmetry Protected Topology in Topological Insulators and Superconductors
• Supersymmetric quantum field theory with exotic symmetry in 3+1 dimensions and fermionic fracton phases
• Higher-order topological phases protected by noninvertible and subsystem symmetries