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Modern Physics Letters B

Field-Induced Phase Transition in S=1 XXZ Chain with Biquadratic Exchange Interaction

Ryutaro Sato

Published Dec 30, 1997• 1 citation
Publisher

Abstract

We study the magnetization process of the S=1 XXZ chain with biquadratic exchange interaction at zero temperature. This system can be regarded as a quantum lattice gas composed of "particles" with Sz=0, ±1. We introduce an approximate nested Bethe ansatz (ANBA) to examine the possibility of phase transition induced by the magnetic field. In the high-magnetization region σ≥σ0 for certain σ0, the ANBA gives the exact ground state energies. For σ<σ0 the ANBA gives approximate solutions. The analysis shows that a phase transition occurs at σ0 across which the magnetic susceptibility changes discontinuously. Comparing with the finite-size diagonalization, we argue that σ0 is the exact critical magnetization.

DOI
10.1142/s0217984997001547

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We study the magnetization process of the S=1 XXZ chain with biquadratic exchange interaction at zero temperature. This system can be regarded as a quantum lattice gas composed of "particles" with Sz=0, ±1. We introduce an approximate nested Bethe ansatz (ANBA) to examine the possibility of phase transition induced by the magnetic field. In the high-magnetization region σ≥σ0 for certain σ0, the ANBA gives the exact ground state energies. For σ<σ0 the ANBA gives approximate solutions. The analysis shows that a phase transition occurs at σ0 across which the magnetic susceptibility changes discontinuously. Comparing with the finite-size diagonalization, we argue that σ0 is the exact critical magnetization.
We investigate magnetization process $(M\ensuremath{-}H\phantom{\rule{0ex}{0ex}}\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{v}\mathrm{e})$ of S=1S=1S=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=1/2XYS=1/2 \mathrm{XY}S=1/2XY 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.
The zero-temperature magnetization curve of the S =1 antiferromagnetic XXZ chain with partial integrability is studied by the Bethe ansatz, combined with a numerical renormalization-group method. We find a magnetic first-order phase transition; the magnetization curve shows a discontinuity at a critical field h c . Due to the partial integrability, the low-field curve and the high-field curve each correspond to a part of the magnetization curve of the S=12S=\frac12S=21​XXZ chain. We conclude that the obtained magnetization curve is exact in the whole range of the magnetic field.
The magnetization processes of the S = 3/2 and S = 2 antiferromagnetic chains with the biquadratic interaction are investigated using the numerical diagonalization of the finite-size cluster. It is found that the system does not exhibit the spin nematic phase, which was predicted to occur for the S = 1 antiferromagnetic chain. Instead, the present analysis reveals that the quantum spin triatic and quatic liquid phases appear below the saturation magnetization for sufficiently large negative biquadratic interaction, for S = 3/2 and S = 2 chains, respectively. In addition it is also found that the magnetization jump up to the saturation magnetization appears for the small negative biquadratic interaction. The phase diagrams with respect to the negative biquadratic interaction and the magnetization are presented for the S = 3/2 and S = 2 antiferromagnetic chains.
Abstract In this paper we investigate the ability of the generalized concurrence as a quantum entanglement measure to describe the quantum and thermal phase transitions in the spin-1 Heisenberg model with bilinear and biquadratic interactions and single-ion anisotropy terms, under a magnetic field. Calculations are performed for two and three spin chains based on the exact diagonalization method. We show that in the near vicinity of the zero temperature, the generalized concurrence changes abruptly from a finite non-zero value to zero by changing the parameters of the model. This is signature of a quantum phase transition that is carefully justified by studying the thermodynamic functions such as magnetization, particle number, particle susceptibility and magnetic susceptibility. The critical points are found and various ordered phases are discussed.
The ground state of the S=1 XXZ spin chain under the influence of the random magnetic field is studied by means of the exact diagonalization method. The S=12 counterpart has been investigated extensively so far. The easy-plane area, including the Haldane and the XY phases, is considered. The area suffers significantly from the magnitude of the constituent spin. Destruction of the Haldane state is observed at a critical strength of the random field, which is comparable to the magnitude of the Haldane gap. This transition is characterized by the disappearance of the string order. The XY region continues until at a critical randomness, at which a transition of the KT-universality class occurs. These features are contrasted with those of the S=12 counterpart.
We study the integrable SU( M ) and SU q ( M ) quantum spin chains in the high-magnetic-field region at zero temperature. For M =4 we found second-order phase transitions at two different fields, H 1 and H 2 . At both transition points, the magnetization curve versus magnetic field has cusps with discontinuities in the magnetic susceptibility. We clarify the mechanism of the phase transitions, from which we conclude that the SU( M ) and S U q ( M ) quantum spin chains undergo ( M -2) times field-induced phase transitions at zero temperature.