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Talk by Peng Rao: "Spin-particle duality and Berry phase of visons in Z2 topologically ordered states"
MPI-PKS Dresden
08.07.2022 at 09:00
Abstract: The Toric Code (TC) is one of the simplest and most illustrative examples of $\mathbb{Z}_2$ topological order, and contains static, non-interacting anyons. More generally, the TC suggests a rewriting of the lattice spin-$1/2$ degrees of freedom in terms of these anyons, and can be used as a building block for constructing new $\mathbb{Z}_2$ topologically ordered states in which anyons can acquire dynamics and interact. In this talk, I will discuss an exact duality between the spin-$1/2$ Hilbert space on a two-dimensional periodic rectangular lattice, and the Hilbert space of $e$-bosons and $\varepsilon$-fermions from the TC. The duality incorporates the mutual semionic statistics of $e$ and $\varepsilon$ (namely they are mutual $\pi$-vortices) and the global topological degrees of freedom due to lattice periodicity. This allows us to construct and study a class of $\mathbb{Z}_2$ topologically ordered states `enriched by translation symmetry’ as topological superconductors of $\varepsilon$-fermions, and classify them in a $\mathbb{Z} \times (\mathbb{Z}_2)^3$ scheme extending the Chern number classification. In addition, I will discuss the Berry phases of $e$-particles (visons) renormalized by the superconducting vacua of these phases, and establish numerically their relations to the underlying topology of the system.
Room A 450 (SHARP)