In this work, we illustrate how a Jordan-Wigner transformation combined with symmetry considerations enables a direct solution of Kitaev's model on the honeycomb lattice. We (i) express the p-wave type fermionic ground states of this system in terms of the original spins, (ii) adduce that symmetry alone dictates the existence of string and planar brane type correlators and their composites, (iii) compute the value of such non-local correlators by employing the Jordan-Wigner transformation, (iv) affirm that the spectrum is inconsequential to the existence of topological quantum order and that such information is encoded in the states themselves, and (v) express the the local symmetries of Kitaev's model and the anyonic character of the excitations in terms of fermions.PACS numbers:
In this work, we show that the quantum compass model on a square lattice can be mapped to a fermionic model with local-density interaction. We introduce a mean-field approximation where the most important fluctuations, those perpendicular to the ordering direction, are taken into account exactly. It is found that the quantum phase transition point at J x = J z marks a first-order phase transition. We also show that the mean-field result is robust against the remaining fluctuation corrections up to the second order.
We report hole-doping dependence of the in-plane resistivity rho(ab) in a cuprate superconductor La(2-x)Sr(x)CuO4, carefully examined using a series of high-quality single crystals. Our detailed measurements find a tendency towards charge ordering at particular rational hole-doping fractions of 1/16, 3/32, 1/8, and 3/16. This observation appears to suggest a specific form of charge order and is most consistent with the recent theoretical prediction of the checkerboard-type ordering of the Cooper pairs at rational doping fractions x = (2m+1)/2n, with integers m and n.
We propose a microscopic state for the vortex phase of BSCO superconductors. Around the vortex core or above H(c2), the d wave hole pairs form a checkerboard localized in the antiferromagnetic background. We discuss this theory in connection with recent STM experiments.
We show that a d-wave ordering in particle-hole channel, dubbed as d-wave checkerboard order, possesses important physics that can sufficiently explain the STM results in cuprates. A weak dwave checkerboard order can effectively suppress the coherence peak in the single-particle spectrum while leaving the spectrum along nodal direction almost unaffected. Simultaneously, it generates a Fermi arc with little dispersion around nodal points at finite temperature that is consistent with the results of ARPES experiments in the pseudogap phase. We also show that there is a general complementary connection between the d-wave checkerboard order and the pair density wave order. Suppressing superconductivity locally or globally through phase fluctuation should induce both orders in underdoped cuprates and explain the nodal-antinodal dichotomy observed in ARPES and STM experiments.
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