Dynamical dimer correlations at bipartite and non-bipartite Rokhsar–Kivelson points
Dynamical dimer correlations at bipartite and non-bipartite Rokhsar–Kivelson points
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二分和非二分 Rokhsar-Kivelson 点的动态二聚体相关性
DOI：
10.1088/1742-5468/2008/01/p01010
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
F. Assaad
中科院分区：
文献类型：
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作者：
A. Läuchli;S. Capponi;F. Assaad
我们确定了二分正方形和立方格子以及非二分三角形格子上量子二聚体模型在Rokhsar-Kivelson点处的动力学二聚体关联函数。基于Henley的算法思想，我们模拟了经典二聚体构型在连续时间内的随机过程，并进行了随机解析延拓，得到了动量空间和频域的动力学关联。这种方法使我们能够直接观察到超越单模近似的布里渊区的色散关系和光谱强度的演变。在正方形晶格上，我们证实了与靠近波矢（π，π）和（π，0）的软模相关的分析预测，并进一步揭示了靠近波矢（0，0）的阴影带的存在。在立方晶格上，光谱也是无间隙的，但这里仅发现（π，π，π）处的单个软模，如通过单模近似所预测的。软模在很长的波长处具有二次色散，但是非常迅速地过渡到线性行为。我们相信这是库仑相的线性色散“光子”的残余。最后，三角形晶格处于完全有间隙的液相中，其中二聚体光谱的底部呈现丰富的结构。在M点处，差距最小，并且光谱响应由尖锐的准粒子峰主导。另一方面，在X点处，谱函数要宽得多。我们勾画了一个可能的解释的基础上交叉的相干二聚体激发到两个vison连续。
We determine the dynamical dimer correlation functions of quantum dimer models at the Rokhsar–Kivelson point on the bipartite square and cubic lattices and the non-bipartite triangular lattice. On the basis of an algorithmic idea by Henley, we simulate a stochastic process of classical dimer configurations in continuous time and perform a stochastic analytical continuation to obtain the dynamical correlations in momentum space and the frequency domain. This approach allows us to observe directly the dispersion relations and the evolution of the spectral intensity within the Brillouin zone beyond the single-mode approximation. On the square lattice, we confirm analytical predictions related to soft modes close to the wavevectors (π,π) and (π,0) and further reveal the existence of shadow bands close to the wavevector (0,0). On the cubic lattice the spectrum is also gapless but here only a single soft mode at (π,π,π) is found, as predicted by the single-mode approximation. The soft mode has a quadratic dispersion at very long wavelength, but crosses over to a linear behavior very rapidly. We believe this to be the remnant of the linearly dispersing ‘photon’ of the Coulomb phase. Finally the triangular lattice is in a fully gapped liquid phase where the bottom of the dimer spectrum exhibits a rich structure. At the M point the gap is minimal and the spectral response is dominated by a sharp quasiparticle peak. On the other hand, at the X point the spectral function is much broader. We sketch a possible explanation based on the crossing of the coherent dimer excitations into the two-vison continuum.