Spin-Fluid to Dimer and Néel to Dimer Phase Transitions in a Spin-1/2 Heisenberg Chain with Competing Interactions
Spin-Fluid to Dimer and Néel to Dimer Phase Transitions in a Spin-1/2 Heisenberg Chain with Competing Interactions
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自旋 1/2 海森堡链中具有竞争相互作用的自旋流体到二聚体和 Néel 到二聚体的相变
DOI：
10.1143/jpsj.61.4665
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发表时间：
1992
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影响因子：
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通讯作者：
M. Kaburagi
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文献类型：
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作者：
T. Tonegawa;I. Harada;M. Kaburagi
图1所示。自旋流体相和二聚体相以及尼尔相和二聚体相之间的相边界线。式中，A (N)为N个自旋的N大小链的单重态-三重态能隙，由A (N)== Eo (Ni 1)-E,(N)给出。对于给定的7和a的集合，用数值方法求解这个方程，我们确定了与N相关的点1'c （N+ 2， N）。然后,extrapolating1'c (N + 2, N)的极限N -) oo通过最小二乘nt结果N = 12, 14日,16日,18岁的二次函数1 / (N + 1),我们估计1 ',对给定的一组7和j。伊辛地区在霁>啊,我们有,如上所述,相变的nnite-gap奈尔阶段hnite-gap二聚体阶段,并相应PRG方程有两个为每个组7和有意义的解决方案,其中一个,另一个是respec-tively,在数值误差范围内，小于和大于1‘，都会导致1’的相同结果。在XY地区,另一方面,无关地的霁的迹象,我们有相变的无间隙的spin-Huid阶段hnite-gap二聚体阶段,因此PRG方程只有一个有意义的解决方案,每组7和我。我们的价值1 ',25 = = O .} O . Ol在海森堡点估计在霁> O同意的情况下,在数值错误,与相应的值1,= = O . 2411} O . OOOI得到Okamoto传闻)和野村和1 'c: O . 246通过Okamoto和上野。i‘)此外，我们在XY区域的当前值1’比我们之前用另一种数值方法得到的相应值要小一些。•6•9)将1′的估计值连接起来，对于7和j的各个集合，我们得到如图1所示的相边界线。值得注意的是，在Ji< O的情况下，XY区域的线可以相当平滑地外推到
Fig. 1.'Phase boundary line between the spin-Huid and dimer phases and that between the Neel and dimer phases. where A (N) denotes the singlet-triplet energy gap for the nnite-size chain of N spins and is given by A (N)== Eo (Ni 1)-E,(N). Solving this equation numerically for a given set of 7 and a, we determine the N-dependent nxed point 1'c (N+ 2, N). Then, extrapolating1'c (N+ 2, N) to the limit of N-) oo by making a least-squares nt of the results for N= 12, 14, 16, 18 to a quadratic function of 1/(N+ 1), we estimate 1', for the given set of 7 and j. In the Ising region in the case of Ji> O, we have, as noted above, the phase transition from the nnite-gap Neel phase to the hnite-gap dimer phase, and correspondingly the PRG equation has two meaningful solutions for each set of 7 and a, one of which and the other are, respec-tively, smaller and larger than l',, both leading to the same result for 1', within numerical error. In the XY region, on the other hand, irrespectively of the sign of Ji, we have the phase transition from the gapless spin-Huid phase to the hnite-gap dimer phase, and thus the PRG equation has only one meaningful solution for each set of 7 and i. Our value 1',== O. 25Å} O. Ol estimated at the Heisenberg point in the case of Ji> O agrees, within numerical error, with the corresponding values 1',== O. 2411Å} O. OOOI obtained by Okamoto and Nomura'O) and 1'c: O. 246 obtained by Okamoto and Ueno. i') Furthermore, our present values of 1', in the XY region are a Iittle bit smaller than the corre-sponding values which we have obtained previously by another numerical method.• 6• 9) Connecting the estimated values of 1', for various sets of 7 and j, we obtain the phase boundary lines shown in Fig. 1. It is noted that the line in the XY region in the case of Ji< O can be extrapolated rather smoothly to
T.Tonekawa：“具有竞争相互作用的一维各向同性自旋 1 海森堡反铁磁体的基态特性”J.Phys.Soc.Jpn。
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