Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B, Condensed matter

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

Djalma Medeiros, G. G. Cabrera

Published Feb 1, 1991• 16 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.43.3703

Related papers

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 matter•Jul 1, 1991•4 citations

Energy gap of theS=1 antiferromagnetic Heisenberg chain

Tôru Sakai, Minoru Takahashi

The S=1 isotropic antiferromagnetic Heisenberg chain is studied by exact diagonalizations using the Lancz\"os algorithm. Energy gaps, structure factors at k=\ensuremath{\pi}, and staggered susceptibilities at T=0 are calculated for finite rings up to N=16, and extrapolated to an infinite system using Shanks' transformation. The estimated energy gap is 0.411\ifmmode\pm\else\textpm\fi{}0.001, which agrees with the result of Monte Carlo calculations by Nightingale and Bl\"ote. Further, it is found that a finite-size correction decays exponentially and the decay constant corresponds with the correlation length, which is about 5.

Physical review. B, Condensed matter•Jul 1, 1990•86 citations

The Haldane Gap of the S = 1 Heisenberg Antiferromagnetic Chain

Hiroki Nakano, Hiroto Tadano, Norikazu Todoroki +1 more

The one-dimensional Heisenberg antiferromagnet of S = 1 spins is studied by numericaldiagonalization method based on the Lanczos algorithm. The Haldane gap of this system isnumerically estimated from finite-size clusters under the twisted boundary condition up tothe 30-site system. The finite-size results are analyzed by a convergence-acceleration technique; the multistep procedure of the convergence acceleration is successfully carried out.The present estimate for the gap magnitude is more precisely than the previously reportedvalue from a Lanczos-diagonalization study. It also agrees well with the result reported ina study based on the density matrix renormalization group calculation. The present studyclarifies that Lanczos-diagonalization calculations can sufficiently contribute for preciselyestimating an energy gap although this method can treat only small clusters.

Journal of the Physical Society of Japan•Jun 1, 2022•10 citations

Finite-lattice extrapolations for a Haldane-gap antiferromagnet

O. Golinelli, Th. Jolicœur, R. Lacaze

We present results of exact diagonalization of the isotropic antiferromagnetic S=1 Heisenberg chain by the Lanczos method, for finite rings of up to N=22 sites. The Haldane gap G(N) and the ground-state energy per site e(N) converge, with increasing N, faster than a power law. By VBS and Shanks transformations, the extrapolated values are G(\ensuremath{\infty})=0.41049(2) and e(\ensuremath{\infty})=-1.401485(2). The spin-spin correlation function is well fit by exp(-r/\ensuremath{\xi})/ \ensuremath{\surd}r with \ensuremath{\xi}=6.2.

arXiv:cond-mat/9402043•Physical review. B, Condensed matter•Aug 1, 1994•142 citations

Numerical study of antiferromagnetic Heisenberg-Ising chains for spin s=1/2

Djalrna Medeiros, G. G. Cabrera

The Heisenberg-Ising Hamiltonian has been exactly solved us- ing the Lanczos method, for chain of up to N = 28 spins. In the whole anisotropic region, the mass gap displays a dominant exponential behavior with size. The extrapolated ground state is doubly degenerate, and presents long-range order with dominant components of the Neel type. Quantum fluctuations become more important as long as the anisotropy is reduced, leading to a disordered singlet ground state for the infinite system at the isotropic point.

•Jan 1, 1991•0 citations

Critical behaviour of spin-s Heisenberg antiferromagnetic chains: analytic and numerical results

Ian K. Affleck, Doron Gepner, Heinz J. Schulz +1 more

A general phase diagram for isotropic antiferromagnetic chains has been proposed recently, using conformal field theory. This is developed further to predict the spectrum of finite chains, including logarithmic corrections. These predictions are tested against Bethe ansatz and exact diagonalisation results for various Hamiltonians with s=1/2, 1 and 3/2. Logarithmic corrections to correlation functions and the scaling of gaps for infinite systems are also given.

Journal of Physics A Mathematical and General•Mar 7, 1989•433 citations
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.
The S=1 isotropic antiferromagnetic Heisenberg chain is studied by exact diagonalizations using the Lancz\"os algorithm. Energy gaps, structure factors at k=\ensuremath{\pi}, and staggered susceptibilities at T=0 are calculated for finite rings up to N=16, and extrapolated to an infinite system using Shanks' transformation. The estimated energy gap is 0.411\ifmmode\pm\else\textpm\fi{}0.001, which agrees with the result of Monte Carlo calculations by Nightingale and Bl\"ote. Further, it is found that a finite-size correction decays exponentially and the decay constant corresponds with the correlation length, which is about 5.
The one-dimensional Heisenberg antiferromagnet of S = 1 spins is studied by numericaldiagonalization method based on the Lanczos algorithm. The Haldane gap of this system isnumerically estimated from finite-size clusters under the twisted boundary condition up tothe 30-site system. The finite-size results are analyzed by a convergence-acceleration technique; the multistep procedure of the convergence acceleration is successfully carried out.The present estimate for the gap magnitude is more precisely than the previously reportedvalue from a Lanczos-diagonalization study. It also agrees well with the result reported ina study based on the density matrix renormalization group calculation. The present studyclarifies that Lanczos-diagonalization calculations can sufficiently contribute for preciselyestimating an energy gap although this method can treat only small clusters.
We present results of exact diagonalization of the isotropic antiferromagnetic S=1 Heisenberg chain by the Lanczos method, for finite rings of up to N=22 sites. The Haldane gap G(N) and the ground-state energy per site e(N) converge, with increasing N, faster than a power law. By VBS and Shanks transformations, the extrapolated values are G(\ensuremath{\infty})=0.41049(2) and e(\ensuremath{\infty})=-1.401485(2). The spin-spin correlation function is well fit by exp(-r/\ensuremath{\xi})/ \ensuremath{\surd}r with \ensuremath{\xi}=6.2.
The Heisenberg-Ising Hamiltonian has been exactly solved us- ing the Lanczos method, for chain of up to N = 28 spins. In the whole anisotropic region, the mass gap displays a dominant exponential behavior with size. The extrapolated ground state is doubly degenerate, and presents long-range order with dominant components of the Neel type. Quantum fluctuations become more important as long as the anisotropy is reduced, leading to a disordered singlet ground state for the infinite system at the isotropic point.