We propose a logical qubit based on the Blume-Capel model: higher spin generalization of Ising chain and which allows for an on-site anisotropy preserving rotational invariance around axis. show that such spin-3/2 model can also support localized Majorana bound states at ends chain. Inspired by known braiding protocols these states, upon appropriate manipulation system parameters, we demonstrat...

Haldane conjectures the fundamental difference in energy spectrum of Heisenberg antiferromagnetic (HAF) spin S chain is that half-integer and integer have gapless gapped spectrums, respectively. The ground state (gs) HAF spin-1/2 spin-1 chains a quasi-long-range short-range correlation, We study effect exchange interaction between an forming normal ladder system its gs properties. inter-chain J...

We construct the fusion operators in the generalized τ -model using the fused L-operators, and verify the fusion relations with the truncation identity. The algebraic Bethe ansatz discussion is conducted on two special classes of τ (2) which include the superintegrable chiral Potts model. We then perform the parallel discussion on the XXZ spin chain at roots of unity, and demonstrate that the s...

The $\mathrm{SL}(2,\mathbb{R})$ Wess-Zumino-Novikov-Witten model realizes bosonic-string theory in ${\mathrm{AdS}}_{3}$ with pure Neveu-Schwarz-Neveu-Schwarz flux. We construct an effective action the semiclassical limit of model, which corresponds to a spin-chain $\ensuremath{\sigma}$-model. adopt two complementary points view. First, we consider classical action. identify fast and slow target...

We discuss generalizations of quantum spin Hamiltonians using anyonic degrees of freedom. The simplest model for interacting anyons energetically favors neighboring anyons to fuse into the trivial ("identity") channel, similar to the quantum Heisenberg model favoring neighboring spins to form spin singlets. Numerical simulations of a chain of Fibonacci anyons show that the model is critical wit...

A model of interacting electrons living on two chains coupled by a transverse hopping t⊥, is solved exactly by bosonization technique. It is shown that t⊥ does modify the shape of the Fermi surface also in presence of interaction, although charge and spin excitations keep different velocities uρ, uσ. Two different regimes occur: at short distances, x ≪ ξ = (uρ − uσ)/4t⊥, the two chain model is ...