A world-line Monte Carlo approach is proposed to calculate the elementary excitations of quantum systems. The lowest energies as a function of momentum are successfully extracted from an imaginary-time correlation function evaluated at a sufficiently low temperature. The method is applied to the antiferromagnetic Heisenberg chains of $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{1}{2},1,\frac{3}{2},$ and $2$ with length up to 64. The spectra for $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{1}{2}$ and 1 coincide well with the result by des Cloizeaux and Pearson and with the result by Takahashi, respectively. The spectra for $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{3}{2}$ and 2 turn out to be massless and massive, respectively. The $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ Haldane gap is estimated to be $0.049\ifmmode\pm\else\textpm\fi{}0.018$.A world-line Monte Carlo approach is proposed to calculate the elementary excitations of quantum systems. The lowest energies as a function of momentum are successfully extracted from an imaginary-time correlation function evaluated at a sufficiently low temperature. The method is applied to the antiferromagnetic Heisenberg chains of $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{1}{2},1,\frac{3}{2},$ and $2$ with length up to 64. The spectra for $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{1}{2}$ and 1 coincide well with the result by des Cloizeaux and Pearson and with the result by Takahashi, respectively. The spectra for $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{3}{2}$ and 2 turn out to be massless and massive, respectively. The $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ Haldane gap is estimated to be $0.049\ifmmode\pm\else\textpm\fi{}0.018$.

Physical Review LettersOct 30, 199551 citations

Excitations in the antiferromagnetic Heisenberg chain

András Sütö

Solid State CommunicationsNov 1, 19765 citations

Elementary excitations of S =1 antiferromagnetic Heisenberg chains with bond alternation

Shoji Yamamoto

A world-line quantum Monte Carlo method is employed to study the elementary excitations of S=1 antiferromagnetic Heisenberg chains with bond alternation described by the Hamiltonian, scrH=J ${\mathit{tsum}}_{\mathit{i}}$ [1-(-1 ${)}^{\mathit{i}}$ \ensuremath{\delta}] ${\mathrm{S}}_{\mathit{i}}$ \ensuremath{\cdot} ${\mathrm{S}}_{\mathit{i}+1}$ . Imaginary-time correlation functions of this system at low-enough temperatures exhibit almost single-exponential decay and thus the lowest excitation spectrum can be successfully extracted from them. As \ensuremath{\delta} increases from 0 to 1, the system encounters a continuous phase transition at \ensuremath{\delta}\ensuremath{\simeq}0.25, where the energy(E)-momentum(q) relation is fitted well to the form E(q)=( ${\mathit{v}}^{2}$ ${\mathrm{sin}}^{2}$ q+${\mathrm{\ensuremath{\Delta}}}^{2}$ ${)}^{1/2}$ with the effective light velocity v=2.46\ifmmode\pm\else\textpm\fi{}0.08 and the energy gap \ensuremath{\Delta} which vanishes in the long chain limit. The central charge c at the massless critical point is estimated to be 1.02\ifmmode\pm\else\textpm\fi{}0.09, which suggests the universality class of the Gaussian model.A world-line quantum Monte Carlo method is employed to study the elementary excitations of S=1 antiferromagnetic Heisenberg chains with bond alternation described by the Hamiltonian, scrH=J ${\mathit{tsum}}_{\mathit{i}}$ [1-(-1${)}^{\mathit{i}}$\ensuremath{\delta}]${\mathrm{S}}_{\mathit{i}}$\ensuremath{\cdot}${\mathrm{S}}_{\mathit{i}+1}$. Imaginary-time correlation functions of this system at low-enough temperatures exhibit almost single-exponential decay and thus the lowest excitation spectrum can be successfully extracted from them. As \ensuremath{\delta} increases from 0 to 1, the system encounters a continuous phase transition at \ensuremath{\delta}\ensuremath{\simeq}0.25, where the energy(E)-momentum(q) relation is fitted well to the form E(q)=(${\mathit{v}}^{2}$ ${\mathrm{sin}}^{2}$q+${\mathrm{\ensuremath{\Delta}}}^{2}$${)}^{1/2}$ with the effective light velocity v=2.46\ifmmode\pm\else\textpm\fi{}0.08 and the energy gap \ensuremath{\Delta} which vanishes in the long chain limit. The central charge c at the massless critical point is estimated to be 1.02\ifmmode\pm\else\textpm\fi{}0.09, which suggests the universality class of the Gaussian model.

Physical review. B, Condensed matterJun 1, 199526 citations

Soft modes in the one-dimensional Heisenberg antiferromagnet near saturation

Michael Durnan Johnson, Michael Fowler

The elementary excitations of the one-dimensional spin-S Heisenberg antiferromagnet near saturation are explained, with special attention to the soft mode, in terms of a gas of interacting magnons. Recent numerical studies of the antiferromagnet in a magnetic field uncovered the presence of the soft mode at a magnetization-dependent wave number for large magnetizations. We show that very near saturation and for large spins the antiferromagnet can be written in terms of a gas of magnons interacting via repulsive \ensuremath{\delta}-function potentials, a system with a known Bethe-ansatz solution. The soft mode can then be explained as a Kohn-anomaly-type excitation above a quasi-Fermi-sea. Other elementary excitations form a particle-hole-type double continuum. The soft mode's apparent physical observability is indicated by a shoulder at the appropriate wave number in the integrated longitudinal intensity.The elementary excitations of the one-dimensional spin-S Heisenberg antiferromagnet near saturation are explained, with special attention to the soft mode, in terms of a gas of interacting magnons. Recent numerical studies of the antiferromagnet in a magnetic field uncovered the presence of the soft mode at a magnetization-dependent wave number for large magnetizations. We show that very near saturation and for large spins the antiferromagnet can be written in terms of a gas of magnons interacting via repulsive \ensuremath{\delta}-function potentials, a system with a known Bethe-ansatz solution. The soft mode can then be explained as a Kohn-anomaly-type excitation above a quasi-Fermi-sea. Other elementary excitations form a particle-hole-type double continuum. The soft mode's apparent physical observability is indicated by a shoulder at the appropriate wave number in the integrated longitudinal intensity.

Physical review. B, Condensed matterAug 1, 198619 citations

S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{1}{2},1,\frac{3}{2},

and

2

with length up to 64. The spectra for

S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{1}{2}

and 1 coincide well with the result by des Cloizeaux and Pearson and with the result by Takahashi, respectively. The spectra for

S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{3}{2}

and 2 turn out to be massless and massive, respectively. The

S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2

Haldane gap is estimated to be $0.049\ifmmode\pm\else\textpm\fi{}0.018$.

A world-line quantum Monte Carlo method is employed to study the elementary excitations of S=1 antiferromagnetic Heisenberg chains with bond alternation described by the Hamiltonian, scrH=J

{\mathit{tsum}}_{\mathit{i}}

[1-(-1

{)}^{\mathit{i}}

\ensuremath{\delta}]

{\mathrm{S}}_{\mathit{i}}

\ensuremath{\cdot}

{\mathrm{S}}_{\mathit{i}+1}

. Imaginary-time correlation functions of this system at low-enough temperatures exhibit almost single-exponential decay and thus the lowest excitation spectrum can be successfully extracted from them. As \ensuremath{\delta} increases from 0 to 1, the system encounters a continuous phase transition at \ensuremath{\delta}\ensuremath{\simeq}0.25, where the energy(E)-momentum(q) relation is fitted well to the form E(q)=(

{\mathit{v}}^{2}

{\mathrm{sin}}^{2}

q+${\mathrm{\ensuremath{\Delta}}}^{2}$

{)}^{1/2}

with the effective light velocity v=2.46\ifmmode\pm\else\textpm\fi{}0.08 and the energy gap \ensuremath{\Delta} which vanishes in the long chain limit. The central charge c at the massless critical point is estimated to be 1.02\ifmmode\pm\else\textpm\fi{}0.09, which suggests the universality class of the Gaussian model.