Studies of elemental substitution effect in spin-gap systems by density matrix renormalization group method

针对高温超导体中的赝隙效应和杂质效应，利用密度矩阵重整化群和精确对角化方法，主要研究了各种具有自旋能隙行为的准一维自旋系统中的元素替代效应。我们考虑了一个具有两个参数的一维自旋模型，次近邻耦合α和键交替β。这个模型可以应用于我们所关心的所有材料，[1]Haldane体系、[2]键交替体系、[3]自旋-Peierls体系和[4]自旋阶梯体系。对纯态和含杂质态进行了一系列计算。主要结果如下：(1)根据能隙、自旋关联长度ζ和弦序参数，α和β对纯体系(尺寸L=∞)的整个空间都属于所谓的霍尔丹相，除了自旋液体的两种极限情况：β=1(无键交替)和α=∞(独立的两个S=1/2 Heise…更多nberg链)。(2)当非磁性杂质掺杂时(L是有限的)，不仅ζ，而且具有&lt；S，e_i&gt；≠_0的态的自旋极化行为与典型的霍尔丹区和自旋-液线附近的自旋极化行为不同。对于前者，ζ和&lt；S、e_i&gt；(即磁激发)与L无关，自旋极化局域在链端(杂质位)附近。同时，由于后者的交错磁化强度分布在整个链条上，并且其幅度随着L的减小而急剧增加。因此，我们看到，即使在高掺杂的情况下，属于Forar类的材料基团[1]和[2]仍然保持了带隙性质，而对于后者，微量的杂质破坏了带隙，导致了反铁磁性长程有序。(3)在该模型中，非公度自旋关联已被预见并部分已知。我们阐明了T=0时整个α-β空间的相图。此外，从量子涨落的角度讨论了实空间和动量空间之间的不可公度不一致性。在上述自旋系统计算结果的基础上，我们将计算推广到电子系统，特别是考虑了高温超导体的赝隙和条带结构。这方面的研究将在下一学期的项目中取得成功。较少

In connection with the pseudogap and impurity effect in high temperature superconductors, we have investigated chiefly elemental substitution effect in various quasi one-dimensional spin systems which show spin-gap behaviors, by using the density matrix renormalization group and exact diagonalization methods. We consider a one-dimensional spin model with two parameters, next-nearest-neighbor coupling α and bond alternation β. This model can be applied to all the materials of our concern, [1] Haldane systems, [2] bond-alternating ones, [3] spin-Peierls ones and [4] spin ladder ones. A series of calculations has been performed for pure states and ones with impurities. Main results are : (1) According to the gap, spin correlation length ζ and the string order parameter, the whole space spanned by α and β for the pure systems (size L=∞ ) belongs to the so-called Haldane phase except for the two limiting cases of 'spin liquid' : β=1 (no bond alternation) and α=∞ (independent two S=1/2 Heise … More nberg chains). (2) When non-magnetic impurities are doped (L is finite) , not only ζ but the behaviors of spin polarization in the states with <S^e_i>≠0 are distinct between the typical Haldane regime and the one near the spin-liquid lines. For the former, ζ and <S^e_i> (namely magnetic excitation) are independent of L and spin polarization is localized near the chain end (impurity site). Meanwhile, for the latter staggered magnetization spreads over the whole chain and its amplitude abruptly increases with decreasing L.Thus, we see that the material groups [1] and [2] belonging to the formar category preserve the gap properties even for highly doping, whereas for [3] and [4] in the latter category a tiny amount of impurity disrupts the gap and leads to an antiferromagnetic long range order. (3) In this model incommensurate spin correlation had been anticipated and partly known. We have elucidated the phase diagram in the whole α-β space for T=0. Moreover, discordance of the incommensurability between the real and momentum spaces has been discussed in the light of quantum fluctuation.Based on the above results for spin systems, we have progressed our calculation to the electronic ones, especially taking account of the pseudogap and stripe structure for high temperaure superconductors. The study in this line will be succeeded in the project of next term. Less