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A Numerical Study of Spin-1/2 Alternating Antiferromagnetic Heisenberg Chains

KIYOMI OKAMOTO

Jan 1, 19860 citations

Comparison between Lanczos and linked cluster methods for the Heisenberg antiferromagnet on a square lattice

Jay D. Mancini, William J. Massano, Robert K. Murawski

Solid State CommunicationsDec 1, 19977 citations

Lanczos calculation for thes=1/2 antiferromagnetic Heisenberg chain up toN=28 spins

Djalma Medeiros, G. G. Cabrera

Highly precise numerical calculations using a variation of the Lanczos method devised by Paige were performed for s=1/2 antiferromagnetic Heisenberg finite chains up to sizes N=28. Several interesting physical quantities, including the ground-state energy, the mass gap, and the spin-wave velocity, were computed and fitted for logarithmic finite-size corrections, as suggested by conformal invariance and Bethe ansatz calculations. A crossover size for a maximum of the spin-wave velocity is predicted for N\ensuremath{\sim}50, well above the current available sizes in a typical Lanczos simulation. A list of our numerical results is given along with extrapolated values using standard algorithms.Highly precise numerical calculations using a variation of the Lanczos method devised by Paige were performed for s=1/2 antiferromagnetic Heisenberg finite chains up to sizes N=28. Several interesting physical quantities, including the ground-state energy, the mass gap, and the spin-wave velocity, were computed and fitted for logarithmic finite-size corrections, as suggested by conformal invariance and Bethe ansatz calculations. A crossover size for a maximum of the spin-wave velocity is predicted for N\ensuremath{\sim}50, well above the current available sizes in a typical Lanczos simulation. A list of our numerical results is given along with extrapolated values using standard algorithms.

Physical review. B, Condensed matterFeb 1, 199116 citations

Numerical test of finite-size corrections for the anisotropic Heisenberg antiferromagnet chain

Djalma Medeiros, G. G. Cabrera

A leading exponential dependence of the mass gap with size has been numerically tested in the whole axial-anisotropy region for the spin-1/2 XXZ antiferromagnetic chain. Exact results for finite chains are obtained via a modified Lanczos method due to Paige, allowing calculations up to N=28 spins. Our results show that the ground state is doubly degenerate and displays long-range order throughout the whole anisotropic regime.

Physical review. B, Condensed matterJul 1, 19914 citations

Numerical Calculations of S=1 Heisenberg Antiferromagnetic Chain

M. Takahashi

Springer proceedings in physicsJan 1, 19920 citations

Numerical solution of spin systems and the S=(1/2 Heisenberg antiferromagnet using guided random walks

Ted Barnes, Geoff J. Daniell

In this paper we describe a numerical method for measuring ground-state expectation values and energies of quantum spin systems. The technique exploits the similarity between the Euclidean-time Schr\"odinger equation and a random walk in state space to generate configurations with a weighted distribution proportional to \ensuremath{\Vert}${\ensuremath{\psi}}_{0}$${\ensuremath{\Vert}}^{2}$. A model application to a single spin is described first, followed by application of the method to the isotropic spin-(1/2 Heisenberg antiferromagnet. For the antiferromagnet we measure the singlet ground-state energy and the singlet-triplet energy gap on chains of up to 48 spins. These results are shown to be in good agreement with energies obtained using Lanczos techniques on chains of up to 20 spins for the energy gap and 24 spins for the ground-state energy.In this paper we describe a numerical method for measuring ground-state expectation values and energies of quantum spin systems. The technique exploits the similarity between the Euclidean-time Schr\"odinger equation and a random walk in state space to generate configurations with a weighted distribution proportional to \ensuremath{\Vert}${\ensuremath{\psi}}_{0}$${\ensuremath{\Vert}}^{2}$. A model application to a single spin is described first, followed by application of the method to the isotropic spin-(1/2 Heisenberg antiferromagnet. For the antiferromagnet we measure the singlet ground-state energy and the singlet-triplet energy gap on chains of up to 48 spins. These results are shown to be in good agreement with energies obtained using Lanczos techniques on chains of up to 20 spins for the energy gap and 24 spins for the ground-state energy.

Physical review. B, Condensed matterMar 1, 198826 citations

Numerical study of antiferromagnetic Heisenberg chains for spin S = ½, using the Lanczos method

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Numerical study of antiferromagnetic Heisenberg chains for spin S = ½, using the Lanczos method

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