Journal of the Physical Society of Japan

World-Line Monte Carlo Study of the Dispersion Relation of anS=1 Antiferromagnetic Heisenberg Chain

Shoji Yamamoto, Seiji Miyashita

Published Aug 15, 1994• 10 citations

Abstract

A world-line quantum Monte Carlo method is employed to study the dispersion relation of an S =1 antiferromagnetic Heisenberg chain. An imaginary-time correlation function is evaluated on a transformed two-dimensional Ising system, and the low-lying energy spectrum is extracted from that. This straightforward method produces a dispersion relation which agrees well with the previous results.

DOI: 10.1143/jpsj.63.2866

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Journal of the Physical Society of Japan

World-Line Monte Carlo Study of the Dispersion Relation of anS=1 Antiferromagnetic Heisenberg Chain

Shoji Yamamoto, Seiji Miyashita

Published Aug 15, 1994• 10 citations

Publisher

Abstract

DOI: 10.1143/jpsj.63.2866

Related papers

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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.

{\mathrm{CuCl}}_{2}

\ensuremath{\cdot}2N(

{\mathrm{C}}_{5}

{\mathrm{D}}_{5}

S=1

antiferromagnetic Heisenberg chain. The rapid increase in autocorrelation times which is seen in the conventional world line method as the imaginary-time spacing decreases is eliminated by the present algorithm.