arXiv 1202.16872012-02-08cond-mat.str-el

双重态$S_{\rm tot}=1/2$基态系统的反铁磁有序

Antiferromagnetic order in systems with doublet $S_{\rm tot}=1/2$ ground states

Sambuddha Sanyal, Argha Banerjee, Kedar Damle, Anders W. Sandvik

备注：: 11 two-column pages; 9 eps figures
发表信息：: Phys. Rev. B 86, 064418 (2012)
DOI：: 10.1103/PhysRevB.86.064418

摘要：

本文用量子投影Monte-Carlo方法研究了二维$S=1/2$反铁磁体在奇数格点$N_{\rm tot}=L^2$上的$S_{\rm tot}=1/2$二重态基态.我们计算的基态自旋纹理$Φ^z(\vec{r}) = <S^z(\vec{r})>_{\uparrow}$在$|G>_{\uparrow}$，这个双重的$S^z_{\rm tot}=1/2$组件，并调查之间的关系$n^z$，这个基态自旋纹理的交错组件的热力学极限，和$m$，热力学极限的大小的交错磁化强度矢量的同一系统中的单线态，甚至$N_{\rm tot}$获得。我们发现两者之间的普遍关系，这是独立的微观细节的晶格级哈密顿量，可以很好地近似由多项式插值公式：$n^z \approx (1/3 - \frac{a}{2} -\frac{b}{4}) m + am^2+bm^3$，与$a \approx 0.288$和$b\approx -0.306$。我们还发现，全自旋织构$Φ^z(\vec{r})$本身是占主导地位的反铁磁波矢附近的傅立叶模式在一个普遍的方式。在分析方面，我们探讨这个问题，使用自旋波理论，一个简单的平均场模型写在每个子晶格的总自旋，和转子模型的$\vec{n}$的动力学。我们发现，自旋波理论再现了$Φ^z(\vec{r})$的这种普适性，对于自旋- $S$反铁磁体给出了$α\approx 0.013$和$β\approx 1.003$的$n^z = (1-α-β/S)m + (α/S)m^2 +{\mathcal O}(S^{-2})$，而对于$S=1/2$反铁磁体，亚晶格自旋平均场理论和转子模型都给出了$n^z = 1/3 m$.我们认为，后者的关系成为渐近精确的无限长范围{ \em未受挫}交换相互作用的限制。

英文摘要：

We use projector Quantum Monte-Carlo methods to study the $S_{\rm tot}=1/2$ doublet ground states of two dimensional $S=1/2$ antiferromagnets on a $L \times L$ square lattice with an odd number of sites $N_{\rm tot}=L^2$. We compute the ground state spin texture $Φ^z(\vec{r}) = <S^z(\vec{r})>_{\uparrow}$ in $|G>_{\uparrow}$, the $S^z_{\rm tot}=1/2$ component of this doublet, and investigate the relationship between $n^z$, the thermodynamic limit of the staggered component of this ground state spin texture, and $m$, the thermodynamic limit of the magnitude of the staggered magnetization vector of the same system in the singlet ground state that obtains for even $N_{\rm tot}$. We find a univeral relationship between the two, that is independent of the microscopic details of the lattice level Hamiltonian and can be well approximated by a polynomial interpolation formula: $n^z \approx (1/3 - \frac{a}{2} -\frac{b}{4}) m + am^2+bm^3$, with $a \approx 0.288$ and $b\approx -0.306$. We also find that the full spin texture $Φ^z(\vec{r})$ is itself dominated by Fourier modes near the antiferromagnetic wavevector in a universal way. On the analytical side, we explore this question using spin-wave theory, a simple mean field model written in terms of the total spin of each sublattice, and a rotor model for the dynamics of $\vec{n}$. We find that spin-wave theory reproduces this universality of $Φ^z(\vec{r})$ and gives $n^z = (1-α-β/S)m + (α/S)m^2 +{\mathcal O}(S^{-2})$ with $α\approx 0.013$ and $β\approx 1.003$ for spin-$S$ antiferromagnets, while the sublattice-spin mean field theory and the rotor model both give $n^z = 1/3 m$ for $S=1/2$ antiferromagnets. We argue that this latter relationship becomes asymptotically exact in the limit of infinitely long-range {\em unfrustrated} exchange interactions.

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