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Physical review. B, Condensed matter

Spin correlation function of theS=1antiferromagnetic Heisenberg chain by the large-cluster-decomposition Monte Carlo method

K. Nomura

Published Aug 1, 1989• 97 citations
Publisher

Abstract

We calculate correlation functions of a one-dimensional spin S=1 antiferromagnetic Heisenberg model by the large-cluster-decomposition Monte Carlo method. We find that the correlation functions are well approximated by modified Bessel functions. This result supports Haldane's conjecture, and the correlation length agrees with that obtained from spin-wave theory using elementary excitation data.

DOI
10.1103/physrevb.40.2421

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We calculate correlation functions of a one-dimensional spin S=1 antiferromagnetic Heisenberg model by the large-cluster-decomposition Monte Carlo method. We find that the correlation functions are well approximated by modified Bessel functions. This result supports Haldane's conjecture, and the correlation length agrees with that obtained from spin-wave theory using elementary excitation data.
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We compute the ground-state spin-spin correlation function for the one-dimensional antiferromagnetic Heisenberg model of spin 1/2, 1, and 3/2. The spin-1 chain has a disordered ground state with a correlation length of 6.2 lattice spacings whereas the spin-1/2 and the spin-3/2 chains both have (ln(r)${)}^{\mathrm{\ensuremath{\sigma}}}$/r decaying correlation functions. The logarithmic corrections are different for the spin-1/2 and the spin-3/2 chains. Finite-size scaling is used to analyze the data for chains of up to 128 spins.
The correlation function \ensuremath{\rho}(l)=〈Siz{S}_{i}^{z}Siz​Si+lz{S}_{i+l}^{z}Si+lz​〉 is calculated for the spin-1 Heisenberg antiferromagnetic chain (H=J${\ensuremath{\Sigma}}_{i}$scrSi{\mathrm{scrS}}_{i}scrSi​scrSi+1{\mathrm{scrS}}_{i+1}scrSi+1​, scrSN+1{\mathrm{scrS}}_{N+1}scrSN+1​\ensuremath{\equiv}scrS1{\mathrm{scrS}}_{1}scrS1​) at the ground state. Using the Monte Carlo method of Hirsch, Sugar, Scalopino, and Blankenbecler we find that \ensuremath{\rho}(l) decays exponentially in contrast to the S=half case where \ensuremath{\rho}(l) decays algebraically. This fact coincides with Haldane's prediction and recent numerical calculations. We calculate the upper bound of elementary excitation from the structure factor using a variational method which resembles the Feynman theory for elementary excitation of liquid 4He^{4}\mathrm{He}4He.
The dynamic-spin-correlation function S(q,\ensuremath{\omega}) is computed for the one-dimensional antiferromagnetic Heisenberg model for S=1/2 and S=1. Imaginary-time correlation functions are evaluated with the quantum Monte Carlo method and the maximum-entropy method is used to continue these results to real frequencies. This technique produces a value for the S=1 Haldane gap that agrees with previous work and also gives a good description of inelastic neutron scatter- ing data for the one-dimensional S=1/2 antiferromagnet CuCl2{\mathrm{CuCl}}_{2}CuCl2​\ensuremath{\cdot}2N(C5{\mathrm{C}}_{5}C5​D5{\mathrm{D}}_{5}D5​).