218 research outputs found

    Fracton Topological Order, Generalized Lattice Gauge Theory and Duality

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    We introduce a generalization of conventional lattice gauge theory to describe fracton topological phases, which are characterized by immobile, point-like topological excitations, and sub-extensive topological degeneracy. We demonstrate a duality between fracton topological order and interacting spin systems with symmetries along extensive, lower-dimensional subsystems, which may be used to systematically search for and characterize fracton topological phases. Commutative algebra and elementary algebraic geometry provide an effective mathematical toolset for our results. Our work paves the way for identifying possible material realizations of fracton topological phases.Comment: 9 pages, 4 figures; 8 pages of appendices, 3 figure

    Operator Spreading in Random Unitary Circuits

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    Random quantum circuits yield minimally structured models for chaotic quantum dynamics, able to capture for example universal properties of entanglement growth. We provide exact results and coarse-grained models for the spreading of operators by quantum circuits made of Haar-random unitaries. We study both 1+1D and higher dimensions, and argue that the coarse-grained pictures carry over to operator spreading in generic many-body systems. In 1+1D, we demonstrate that the out-of-time-order correlator (OTOC) satisfies a biased diffusion equation, which gives exact results for the spatial profile of the OTOC, and the butterfly speed vBv_{B}. We find that in 1+1D the `front' of the OTOC broadens diffusively, with a width scaling in time as t1/2t^{1/2}. We address fluctuations in the OTOC between different realizations of the random circuit, arguing that they are negligible in comparison to the broadening of the front. Turning to higher D, we show that the averaged OTOC can be understood exactly via a remarkable correspondence with a classical droplet growth problem. This implies that the width of the front of the averaged OTOC scales as t1/3t^{1/3} in 2+1D and t0.24t^{0.24} in 3+1D (KPZ exponents). We support our analytic argument with simulations in 2+1D. We point out that, in a lattice model, the late time shape of the spreading operator is in general not spherical. However when full spatial rotational symmetry is present in 2+1D, our mapping implies an exact asymptotic form for the OTOC in terms of the Tracy-Widom distribution. For an alternative perspective on the OTOC in 1+1D, we map it to the partition function of an Ising-like model. As a result of special structure arising from unitarity, this partition function reduces to a random walk calculation which can be performed exactly. We also use this mapping to give exact results for entanglement growth in 1+1D circuits.Comment: 29 pages, 16 figures. v2: new appendix on 'mean field

    Majorana Fermion Surface Code for Universal Quantum Computation

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    We introduce an exactly solvable model of interacting Majorana fermions realizing Z2Z_{2} topological order with a Z2Z_{2} fermion parity grading and lattice symmetries permuting the three fundamental anyon types. We propose a concrete physical realization by utilizing quantum phase slips in an array of Josephson-coupled mesoscopic topological superconductors, which can be implemented in a wide range of solid state systems, including topological insulators, nanowires or two-dimensional electron gases, proximitized by ss-wave superconductors. Our model finds a natural application as a Majorana fermion surface code for universal quantum computation, with a single-step stabilizer measurement requiring no physical ancilla qubits, increased error tolerance, and simpler logical gates than a surface code with bosonic physical qubits. We thoroughly discuss protocols for stabilizer measurements, encoding and manipulating logical qubits, and gate implementations.Comment: 17 pages, 13 figure

    Application of colloidal unimolecular polymer (CUP) particles in coatings

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    Colloidal unimolecular polymer (CUP) particles were prepared by the process of water reduction on copolymers containing hydrophobic and hydrophilic monomers at definite ratio using free radical polymerization. The CUPs are formed by the effect of hydrophilic /hydrophobic interactions of the polymer with a change in the solvent environment around them. Once formed these colloidal particles are thermodynamically stable with collapsed hydrophobic groups forming a spheroidal core and hydrophilic charges on the surface stabilizing the particle by the charge repulsion. CUPs contain only the charged CUP particles, water and counterions with all the functionality on the surface for further chemistry. CUP suspension with amine functional groups on the surface can react with epoxy groups and therefore can be used as a crosslinker for 2K epoxy coating. The cured films had comparable properties with commercial amine crosslinker at reduced VOCs. New regulations which reduce the level of volatile organic compounds (VOC) for architectural latex coatings usually necessitate a sacrifice in performance. The use of glycol has been shown to aid in both freeze thaw and wet edge retention. Loss of this VOC will therefore compromise both. With small particle size, CUPs offer a large amount of surface area with the large amount of non-freezable surface water. The presence of non-freezing surface water make CUPs a candidate as an additive for the wet edge retention and freeze thaw stabilizer for architectural paints. The use of CUP as wet edge retention additive and freeze thaw stabilizer is good alternative for the glycols used in paints and therefore lowers the VOC of architectural latex paints --Abstract, page iv
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