Adsorption on Carbon Nanotubes: Quantum Spin Tubes, Magnetization Plateaus, and Conformal Symmetry

Green, Dmitry; Chamon, Claudio

doi:10.1103/physrevlett.85.4128

Cited by 9 publications

(13 citation statements)

References 10 publications

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“…Instead, it is a crystal containing a dilute array of quantum-fluctuating strings, which we call "stripe-walls" since each has a deficit of fermion density and is a domain wall of the crystal order 29 . There is no previous literature on such stripewalls in the case of the triangular lattice for fermions, only for hardcore bosons (in the context of 4 He adsorbed on carbon nanotubes 20,21 . Nevertheless, it was shown in Ref.…”

Section: Van Eertenmentioning

confidence: 99%

“…Past studies 15,20 showed that a single stripe-wall can be mapped exactly to a one-dimensional chain with noninteracting spinless fermions at half filling, with their hopping amplitude equal to t = 1. This mapping remains valid in the supersymmetric case, since all the accessible configurations for the stripe-wall have equal (and maximal) potential energy F .…”

Section: Van Eertenmentioning

confidence: 99%

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Order and supersymmetry at high filling zero-energy states on the triangular lattice

2012

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We perform exact diagonalization studies in d = 2 dimensions for the Fendley and Schoutens model of hard-core and nearest-neighbor excluding fermions that displays an exact non-relativistic supersymmetry. Using clusters of all possible shapes up to 46 sites, we systematically study the behavior of the ground state phase diagram as a function of filling. We focus on the highly degenerate zero-energy states found at fillings between 1/7 and ∼ 1/5. At the lower end of that interval, at filling 1/7, we explicitly show that the ground states are gapped crystals. Consistent with previous suggestions, we find that the extensive entropy of zero states peaks at a filling of ∼ 0.178. At the higher end of the interval, we find zero energy ground states at fillings above 1/5, in contradiction to previous numerical studies and analytical suggestions; these display non-trivial amplitude degeneracies.

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Section: Van Eertenmentioning

confidence: 99%

Section: Van Eertenmentioning

confidence: 99%

Order and supersymmetry at high filling zero-energy states on the triangular lattice

2012

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“…35 Finally, the same code is adaptable, almost without modifications, to the triangular lattice. That may model 3 He or 4 He atoms adsorbed on graphite or on carbon nanotubes, 19,20 which implement a periodic boundary condition in one direction. s h (L x , L y ) be the number of basis states (per k vector) in a configuration with s stripes and h holes on it.…”

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confidence: 99%

Stripes and holes in a two-dimensional model of spinless fermions or hardcore bosons

Zhang

Henley

2003

Phys. Rev. B

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We consider a Hubbard-like model of strongly-interacting spinless fermions and hardcore bosons on a square lattice, such that nearest neighbor occupation is forbidden. Stripes (lines of holes across the lattice forming antiphase walls between ordered domains) are a favorable way to dope this system below half-filling. The problem of a single stripe can be mapped to a spin-1/2 chain, which allows understanding of its elementary excitations and calculation of the stripe's effective mass for transverse vibrations. Using Lanczos exact diagonalization, we investigate the excitation gap and dispersion of a hole on a stripe, and the interaction of two holes. We also study the interaction of two, three, and four stripes, finding that they repel, and the interaction energy decays with stripe separation as if they are hardcore particles moving in one (transverse) direction. To determine the stability of an array of stripes against phase separation into particle-rich phase and hole-rich liquid, we evaluate the liquid's equation of state, finding the stripe-array is not stable for bosons but is possibly stable for fermions.

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“…This paper contains a detailed account of the results in Ref. [10], as well as new analytical results that explain the numerical findings of the previous work.…”

Section: Introductionmentioning

confidence: 60%

Geometric frustration and magnetization plateaus in quantum spin and Bose-Hubbard models on tubes

Green

Chamon

2002

Phys. Rev. B

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We study XXZ Heisenberg models on frustrated triangular lattices wrapped around a cylinder. In addition to having interesting magnetic phases, these models are equivalent to Bose-Hubbard models that describe the physical problem of adsorption of noble gases on the surface of carbon nanotubes. We find analytical results for the possible magnetization plateau values as a function of the wrapping vectors of the cylinder, which in general introduce extra geometric frustration besides the one due to the underlying triangular lattice. We show that for particular wrapping vectors (N, 0), which correspond to the zig-zag nanotubes, there is a macroscopically degenerate ground state in the classical Ising limit. The Hilbert space for the degenerate states can be enumerated by a mapping first into a path in a square lattice wrapped around a cylinder (a Bratteli diagram), and then to free fermions interacting with a single ZN degree of freedom. From this model we obtain the spectrum in the anisotropic Heisenberg limit, showing that it is gapless. The continuum limit is a c = 1 conformal field theory with compactification radius R = N set by the physical tube radius. This result cannot be checked against a Lieb-Schultz-Mattis argument, for the argument is inconclusive when applied to this problem. We show that the compactification radius quantization is exact in the projective J ⊥ /Jz ≪ 1 limit, and that higher order corrections reduce the value of R. The particular case of a (N = 2, 0) tube, which corresponds to a 2-leg ladder with cross links, is studied separately and shown to be gapped because the fermion mapped problem contains superconducting pairing terms.

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Adsorption on Carbon Nanotubes: Quantum Spin Tubes, Magnetization Plateaus, and Conformal Symmetry

Cited by 9 publications

References 10 publications

Order and supersymmetry at high filling zero-energy states on the triangular lattice

Order and supersymmetry at high filling zero-energy states on the triangular lattice

Stripes and holes in a two-dimensional model of spinless fermions or hardcore bosons

Geometric frustration and magnetization plateaus in quantum spin and Bose-Hubbard models on tubes

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