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Physical review. B, Condensed matter

Magnetization process of bilinear-biquadratic spin chains at finite temperature

Kouichi Okunishi

Published Aug 1, 1999• 17 citations
Publisher

Abstract

We investigate magnetization process $(M\ensuremath{-}H\phantom{\rule{0ex}{0ex}}\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{v}\mathrm{e})$ of $S=1$ bilinear-biquadratic (BLBQ) spin chain near critical fields at finite temperatures. We use the density matrix renormalization group (DMRG) for the two-dimensional classical lattice model mapped by the Trotter decomposition, with a help of the Baxter's variational principle. By comparing the DMRG result of $S=1/2 \mathrm{XY}$ chain with the exact solution, we show that the DMRG is an efficient tool to calculate the $M\ensuremath{-}H$ curve at finite temperatures. Further, we compute the $M\ensuremath{-}H$ curve of the BLBQ chain. We compare the DMRG curve of the magnetization process of the BLBQ chain with those obtained by analytic approaches: correctly mapped $\ensuremath{\delta}$-function Bose-gas approach and ``Bethe-ansatz approximation'' approach. Near the saturation field, we show that the $\ensuremath{\delta}$-function Bose gas and the Bethe-ansatz approximation describe the $M\ensuremath{-}H$ curve well in both at zero temperature and finite temperatures. Near the lower critical field, we find that the $\ensuremath{\delta}$-function Bose gas is a good effective model at the Heisenberg point. We further find that the $\ensuremath{\delta}$-function Bose gas cannot describe the $M\ensuremath{-}H$ curve at finite temperatures, near the special point where the $M\ensuremath{-}H$ curve changes qualitatively.

DOI
10.1103/physrevb.60.4043

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