Non-Abelian bosonization of the frustrated antiferromagnetic spin-1/2 chain
Non-Abelian bosonization of the frustrated antiferromagnetic spin-1/2 chain
复制标题
受挫反铁磁自旋 1/2 链的非阿贝尔玻色化
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
D. Sénéchal
中科院分区：
文献类型：
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作者：
D. Allen;D. Sénéchal
我们研究了${mathrm{ensuremath{kappa}}}_{1}$和${mathrm{ensuremath{kappa}}}_{1}$中最近邻（${mathrm{ensuremath{kappa}}}}_{2}$）相互作用的自旋-1/2链，这相当于两条具有“之”形相互作用的链。在连续体极限下，用两个耦合的一级wss - zumino - witten场理论来描述该系统。我们用四个非临界Ising模型（Majorana费米子）说明了它的等价性。这个描述是用来研究缺口的开口作为${mathm {ensuremath{kappa}}}_{1}$的函数和相关的奇偶性自发击穿。我们计算了连续体极限波矢量附近的动态自旋结构因子。我们注释了非零字符串序参数，并通过对微观哈密顿量的非局部变换证明了隐藏的${mathrm{Z}}_{2}$ifmmode imeselse exttimesfi{}${mathrm{Z}}_{2}$对称性的存在。对于铁磁链间耦合，在自旋-单重态和自旋-三重态激发速度不同的情况下，该模型被认为是临界的。
We study the spin-1/2 chain with nearest-neighbor (${mathrm{ensuremath{kappa}}}_{1}$) and next-nearest-neighbor (${mathrm{ensuremath{kappa}}}_{2}$) interactions in the regime ${mathrm{ensuremath{kappa}}}_{2}$ensuremath{gg}:${mathrm{ensuremath{kappa}}}_{1}$, which is equivalent to two chains with a ``zigzag' interaction. In the continuum limit, this system is described in terms of two coupled level-1 Wess-Zumino-Witten field theories. We illustrate its equivalence with four off-critical Ising models (Majorana fermions). This description is used to investigate the opening of a gap as a function of ${mathrm{ensuremath{kappa}}}_{1}$ and the associated spontaneous breakdown of parity. We calculate the dynamic spin structure factor near the wave vectors accessible to the continuum limit. We comment on the nonzero string order parameter and show the presence of a hidden ${mathrm{Z}}_{2}$ifmmode imeselse exttimesfi{}${mathrm{Z}}_{2}$ symmetry via a nonlocal transformation on the microscopic Hamiltonian. For a ferromagnetic interchain coupling, the model is conjectured to be critical, with different velocities for the spin-singlet and spin-triplet excitations.