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Progress of Theoretical Physics

Analytical and Numerical Investigations of Spin Chains

Masaki Takahashi

Published Jan 1, 1994• 8 citations
Publisher

Abstract

Numerical and analytical investigations of one-dimensional Heisenberg model with nearest neighbor interaction are reviewed. These contain Bethe-ansatz method, exact diagonalization calculation, quantum Monte Carlo calculation and field theoretical method. We mainly concern spin-1/2 and spin-1 cases.
DOI
10.1143/ptp.91.1

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Results of a numerical experiment on one-dimensional quantum spin chains are reported. The Heisenberg model with a nearest-neighbor interaction is investigated for spins 1/2\ensuremath{\le}S\ensuremath{\le}2. The procedure of measurement in the conventional checkerboard world-line algorithm is modified to give lower systematic errors. In addition to spatial-correlation properties, the magnon spectral density is extracted from the magnon Green function via the fast maximum-entropy algorithm. In particular, the existence of the Haldane gap in S=1 and S=2 cases is explicitly demonstrated. Hidden antiferromagnetic order peculiar to the Haldane phase is measured for S=1 as a function of one-site anisotropy. The mapping onto the restricted solid-on-solid model is analyzed. The difference between systems with even and odd integer spins is discussed.
We study the magnetic properties of two types of one-dimensional XXXXXX spin-12\frac{1}{2}21​ chains. The first type has only nearest-neighbor interactions which can be either antiferromagnetic or ferromagnetic, and the second type has both nearest-neighbor and next-nearest-neighbor interactions, but only antiferromagnetic in character. We study these systems in the presence of low magnetic fields both analytically and numerically. Comparison of results shows a close relation between the two systems, which is in agreement with results previously found in Heisenberg chains by means of a numerical real-space renormalization-group procedure.