2,143 research outputs found
Criticality in Translation-Invariant Parafermion Chains
In this work we numerically study critical phases in translation-invariant
parafermion chains with both nearest- and next-nearest-neighbor
hopping terms. The model can be mapped to a 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 clock models.
For we match the numerical results to the known conformal field
theory(CFT) identification. We then analyze in detail the phase diagram of a
chain with both nearest and next-nearest neighbor hopping and six
critical phases with central charges being , 1 or 2 are found. We find
continuous phase transitions between and phases, while the phase
transition between and is conjectured to be of
Kosterlitz-Thouless type.Comment: published versio
Topology and Criticality in Resonating Affleck-Kennedy-Lieb-Tasaki loop Spin Liquid States
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
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
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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