2,143 research outputs found

    Criticality in Translation-Invariant Parafermion Chains

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    In this work we numerically study critical phases in translation-invariant ZN\mathbb{Z}_N parafermion chains with both nearest- and next-nearest-neighbor hopping terms. The model can be mapped to a ZN\mathbb{Z}_N spin model with nearest-neighbor couplings via a generalized Jordan-Wigner transformation and translation invariance ensures that the spin model is always self-dual. We first study the low-energy spectrum of chains with only nearest-neighbor coupling, which are mapped onto standard self-dual ZN\mathbb{Z}_N clock models. For 3≤N≤63\leq N\leq 6 we match the numerical results to the known conformal field theory(CFT) identification. We then analyze in detail the phase diagram of a N=3N=3 chain with both nearest and next-nearest neighbor hopping and six critical phases with central charges being 4/54/5, 1 or 2 are found. We find continuous phase transitions between c=1c=1 and c=2c=2 phases, while the phase transition between c=4/5c=4/5 and c=1c=1 is conjectured to be of Kosterlitz-Thouless type.Comment: published versio

    Topology and Criticality in Resonating Affleck-Kennedy-Lieb-Tasaki loop Spin Liquid States

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    We exploit a natural Projected Entangled-Pair State (PEPS) representation for the resonating Affleck-Kennedy-Lieb-Tasaki loop (RAL) state. By taking advantage of PEPS-based analytical and numerical methods, we characterize the RAL states on various two-dimensional lattices. On square and honeycomb lattices, these states are critical since the dimer-dimer correlations decay as a power law. On kagome lattice, the RAL state has exponentially decaying correlation functions, supporting the scenario of a gapped spin liquid. We provide further evidence that the RAL state on the kagome lattice is a Z2\mathbb{Z}_2 spin liquid, by identifying the four topological sectors and computing the topological entropy. Furthermore, we construct a one-parameter family of PEPS states interpolating between the RAL state and a short-range Resonating Valence Bond state and find a critical point, consistent with the fact that the two states belong to two different phases. We also perform a variational study of the spin-1 kagome Heisenberg model using this one-parameter PEPS.Comment: 10 pages, 14 figures, published versio

    Chiral projected entangled-pair state with topological order

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    We show that projected entangled-pair states (PEPS) can describe chiral topologically ordered phases. For that, we construct a simple PEPS for spin-1/2 particles in a two-dimensional lattice. We reveal a symmetry in the local projector of the PEPS that gives rise to the global topological character. We also extract characteristic quantities of the edge conformal field theory using the bulk-boundary correspondence.Comment: 11 pages, 7 figure
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