We used a combination of the quantum Monte Carlo technique and the maximum entropy method to calculate the dynamic structure factor of the quantum Heisenberg antiferromagnet. The dynamics is governed by renormalized damped spin waves and we calculate their frequencies and linewidths. The computed spin-wave dispersion is in quantitative agreement with inelastic-neutron-scattering experiments on ${\mathrm{La}}_{2}$ ${\mathrm{CuO}}_{4}$ . The low-energy sector exhibits scaling behavior with the characteristic frequency scale, which is inversely proportional to the correlation length.We used a combination of the quantum Monte Carlo technique and the maximum entropy method to calculate the dynamic structure factor of the quantum Heisenberg antiferromagnet. The dynamics is governed by renormalized damped spin waves and we calculate their frequencies and linewidths. The computed spin-wave dispersion is in quantitative agreement with inelastic-neutron-scattering experiments on ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$. The low-energy sector exhibits scaling behavior with the characteristic frequency scale, which is inversely proportional to the correlation length.

Physical Review LettersMar 16, 199251 citations

Dynamic structure factor of the square-lattice S=1/2 Heisenberg antiferromagnet

Hui Shao, Yanqi Qin, Zi Yang Meng +1 more

Bulletin of the American Physical SocietyMar 13, 20170 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.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 matterJul 1, 199086 citations

Monte Carlo calculation of elementary excitation of spin chains

Minoru Takahashi

An efficient Monte Carlo method is proposed to calculate the elementary excitation spectrum of quantum systems. The lowest energy with arbitrary momentum is obtained by the projector Monte Carlo method. This is applied to the spin-(1/2 and -1 Heisenberg antiferromagnetic chain with length 32. For the S=(1/2 case, the spectrum coincides completely with the spectrum of des Cloiseaux and Pearson. For the S=1 case, the spectrum has a gap at momentum \ensuremath{\pi} as was predicted by Haldane. The value of the gap coincides with the calculation of Nightingale and Blote. The spectrum satisfies a variational relation with the structure factor.An efficient Monte Carlo method is proposed to calculate the elementary excitation spectrum of quantum systems. The lowest energy with arbitrary momentum is obtained by the projector Monte Carlo method. This is applied to the spin-(1/2 and -1 Heisenberg antiferromagnetic chain with length 32. For the S=(1/2 case, the spectrum coincides completely with the spectrum of des Cloiseaux and Pearson. For the S=1 case, the spectrum has a gap at momentum \ensuremath{\pi} as was predicted by Haldane. The value of the gap coincides with the calculation of Nightingale and Blote. The spectrum satisfies a variational relation with the structure factor.

Physical Review LettersMay 8, 1989202 citations

{\mathrm{La}}_{2}

{\mathrm{CuO}}_{4}

. The low-energy sector exhibits scaling behavior with the characteristic frequency scale, which is inversely proportional to the correlation length.