Thermodynamics of random-exchange Heisenberg antiferromagnetic chains

Bondeson, S. R.; Soos, Z. G.

doi:10.1103/physrevb.22.1793

Cited by 74 publications

(17 citation statements)

References 41 publications

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“…Such a situation is usually described within the random-exchange Heisenberg antiferromagnetic chain model first studied in detail by Bondeson and Soos. 55,56 The appropriate Hamiltonian is then given by…”

Section: Random Exchange Modelmentioning

confidence: 99%

Electron spin resonance of doped chalcogenide nanotubes

et al. 2003

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Section: Random Exchange Modelmentioning

confidence: 99%

Electron spin resonance of doped chalcogenide nanotubes

et al. 2003

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“…The major improvements include a bit representation of V B diagrams, bit manipulations for constructing sparse matrices, and a new coordinate relaxation method for finding low-lying states of unsymmetric sparse matrices. We demonstrate exact results for Heisenberg chains and rings of N = 2 0 with only C, symmetry, whereas direct methods [7] have only been applied to symmetric rings of N 5 12. The corresponding limitation of N 5 8 for PPP or Hubbard models becomes N 5 14 with the present method.…”

Section: Introductionmentioning

confidence: 89%

“…(3) or (4) on any V B diagram Ik) leads to hkj coefficients in Eq. (1) according to previously published rules for ionic [lo] and spin [5] problems.…”

Section: B Dimensionality and Linear Independencementioning

confidence: 99%

“…It is advantageous to store BI;P' as a single Ns(2n)-component vector. The rules [ 5 ] for covalent diagrams result in…”

Section: Bond Vectors and Longer-range Interactionsmentioning

confidence: 99%

“…There have been many treatments [3] in which I k ) was either expanded in terms of Slater determinants thereby losing the compact representation of S eigenstates, or matrix elements (k'lXlk) were computed directly for the nonorthogonal states. We have pursued instead diagrammatic VB methods in which the Ik) are basis vectors to obtain energies, bond orders, charges, transition moments, and other properties of exact correlated states for larger N, and N in one-dimensional PPP [4], Heisenberg [5], and various Hubbard models [6].…”

Section: Introductionmentioning

confidence: 99%

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Diagrammatic valence‐bond theory for finite model Hamiltonians

Ramasesha

Soos

1984

Int J of Quantum Chemistry

Self Cite

103

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Valence bond (VB) diagrams form a complete basis for model Hamiltonians that conserve total spin, S, and have one valence state, +p, per site. Hubbard and Pariser-Parr-Pople (PPP) models illustrate ionic problems, with zero, one, or two electrons in each 4 , while isotropic Heisenberg models illustrate spin problems, with only purely covalent V B diagrams. The difficulty of nonorthogonal V B diagrams is by-passed by exploiting the finite dimensionality of the complete basis and working with unsymmetric sparse matrices. We introduce efficient bit manipulations for generating, storing, and handling V B diagrams as integers and describe a new coordinate relaxation method for the ground and lowest excited states of unsymmetric sparse matrices. Antiferromagnetic spin-; Heisenberg rings and chains of N S 2 0 spins, or 2N spin functions, are solved in C, symmetry as illustrative examples. The lowest S = 1 and 0 excitations are related to domain walls, or spin solitons, and studied for alternations correiponding to polyacetylene. V B diagrams with arbitrary S and nonneighbor interactions are constructed for both spin and ionic problems, thus extending diagrammatic VB theory to other topologies.

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The valence bond calculations for conjugated hydrocarbons having 24-28 ?-electrons

Jiang

2000

J. Comput. Chem.

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A novel algorithm is introduced for coding all Slater determinants in the covalent space with conserved S Z , the z component of total spin S for a classical valence bond (VB) model. It effectively minimizes the search time and the storing space in the central memory of the computer. In cooperation with symmetry reductions based on molecular point group and spin inversion, the VB calculations have been extended to benzenoid hydrocarbons of up to 28 π-electrons that have 4 × 10 7 configurations. The low-lying states of benzenoids with 24, 26, and 28 π-electrons have been obtained for 62 species. To rationalize the aromaticity of benzenoids in a VB scheme, the resonance energy per hexagon (REPH) is defined. A linear correlation between the REPH and the energy gap of the ground (singlet) state and the first excited (triplet) state for 89 benzenoids is established. Contract/grant sponsor: China NSF bases in S = 0 space they treated contained 208,012 configurations. Meanwhile, Soos 6 and coworkers developed the diagrammatic approach jointly with symmetry reductions in S space to deal with molecules of 10 6 configurations in the framework of the PPP scheme. Cioslowski 7 has advanced an efficient computational algorithm to solve the VB Hamiltonian of linear polyenes with up to 18 electrons. Meanwhile, ab inito VB calculations have been carried out for 10 π-electron systems, such as naphthalene and azulene. 8 Recently, our group employed the Lanczos method 9 to implement VB calculations in S Z space. The low-lying states of benzenoid hydrocarbons

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Thermodynamics of random-exchange Heisenberg antiferromagnetic chains

Cited by 74 publications

References 41 publications

Electron spin resonance of doped chalcogenide nanotubes

Electron spin resonance of doped chalcogenide nanotubes

Diagrammatic valence‐bond theory for finite model Hamiltonians

The valence bond calculations for conjugated hydrocarbons having 24-28 ?-electrons

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