Calculations of the thermodynamic quantities, and the spectra of spinons, triplet excitations, and two-particle spin-singlet (Δ S z = 0,±1) excitations for a weakly coupled antiferromagnetic S = 1/2 spin chain are made using a mean-field approximation for the interchain couplings ( J 2 ) by the quantum Monte Carlo method. The mass gaps in these excitation spectra are estimated as functions of the interchain coupling. The critical field H c , and the temperatures at which the spinon and singlet gaps close ( T 1 and T 2 , respectively) are obtained. Some peculiarities of the staggered magnetization, the specific heat, and the spin-spin correlation function are found at T 1 = 0.9 J 2 , T 2 = 1.5 J 2 , H c = 3.8 J 2 , as determined by linear function fitting for J 2 / J 1 <0.15. The intrachain and interchain couplings, and the staggered magnetization for KCuF 3 , Sr 2 CuO 3 , and Ca 2 CuO 3 are estimated, and mass gaps are predicted to exist in the spectra of the spinons and the singlet two-particle excitations.
We study the low-temperature properties of S = 1 and S = 1/2 alternating spin chains with antiferromagnetic nearest-neighbour exchange couplings using analytical techniques as well as a quantum Monte Carlo method. The spin-wave approach predicts two different low-lying excitations, which are gapped and gapless, respectively. The structure of low-lying levels is also discussed using perturbation theory in terms of the strength of the Ising anisotropy. These analytical findings are compared with the results of quantum Monte Carlo calculations, and it turns out that spin-wave theory describes the present system well. We conclude that the quantum ferrimagnetic chain exhibits both ferromagnetic and antiferromagnetic aspects.
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
tsumi [1-(-1
)i\ensuremath{\delta}]
Si\ensuremath{\cdot}
Si+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)=(
v2 sin2q+${\mathrm{\ensuremath{\Delta}}}^{2}$
)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.
Heisenberg antiferromagnetic spin ``ladders'' (two coupled spin chains) are low-dimensional magnetic systems which for S=1/2 interpolate between half-integer-spin chains, when the chains are decoupled, and effective integer-spin one-dimensional chains in the strong-coupling limit. The spin-1/2 ladder may be realized in nature by vanadyl pyrophosphate, (VO
)2P2O7. In this paper we apply strong-coupling perturbation theory, spin-wave theory, Lanczos techniques, and a Monte Carlo method to determine the ground-state energy and the low-lying excitation spectrum of the ladder. We find evidence of a nonzero spin gap for all interchain couplings ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$>0. A band of spin-triplet excitations above the gap is also analyzed. These excitations are unusual for an antiferromagnet, since their long-wavelength dispersion relation behaves as (k-
k0)2 (in the strong-coupling limit ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\gg}J, where J is the in-chain antiferromagnetic coupling). Their band is folded, with a minimum energy at
k0=\ensuremath{\pi}, and a maximum between
k1=\ensuremath{\pi}/2 (for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$=0) and 0 (for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$=\ensuremath{\infty}). We also give numerical results for the dynamical structure factor S(q,\ensuremath{\omega}), which can be determined in neutron scattering experiments. Finally, possible experimental techniques for studying the excitation spectrum are discussed.
We give a full description of a recently developed efficient Monte Carlo Approach to low-lying excitations of one-dimensional quantum spin systems. The idea is in a word expressed as extracting the lower edge of the excitation spectrum from imaginary-time quantum Monte Carlo data at a sufficiently low temperature. First, the method is applied to the antiferromagnetic Heisenberg chains of S=1/2, 1, 3/2, and 2. In the cases of S=1/2 and S=1, comparing the present results with the previous findings, we discuss the reliability of the method. The spectra for S=3/2 and S=2 turn out to be massless and massive, respectively. In order to demonstrate that our method is very good at treating long chains, we calculate the S=2 chain with length up to 512 spins and give a precise estimate of the Haldane gap. Second, we show its fruitful use in studying quantum critical phenomena of bond-alternating spin chains. Using the conformal invariance of the system as well, we calculate the central charge of the critical S=1 chain, which results in the Gaussian universality class. Third, we study an alternating-spin system composed of two kinds of spins S=1 and 1/2, which shows the ferrimagnetic behavior. We find a quadratic dispersion relation in the small-momentum region. The numerical findings are qualitatively explained well in terms of the spin-wave theory. Finally, we argue a possibility of applying the method to the higher excitations, where we again deal with the S=1 Heisenberg antiferromagnet and inquire further into its unique low-energy structure. All the applications demonstrate the wide applicability of the method and its own advantages.