Geometrical Frustration in Strongly Correlated Electron Systems

二维量子三角海森堡模型的低能特性研究最近，清水等人。报道了在κ-(Et)2Cu2(CN)3三角形晶格上，自旋为S=1/2的有机Mott绝缘体中，没有观察到低至32mK的磁性LRO。他们的实验结果表明，包括自旋液体在内的一种新的基态是可能的。随后，Nakatsuji et al.研究发现，在准2D量子三角结构NiGa2S4中，尽管存在较强的非铁磁相互作用，但在0.35K下仍没有LRO的迹象。在后一个系统中，比热系数C在足够低的温度下表现为二次温度依赖关系，在低温区的均匀自旋磁化率是恒定的，这表明存在低激发态的无质量激发。在这些实验结果的激励下，我们研究了零温下量子三角海森堡反铁磁体在零温量子相变附近的二维低温性质。利用O(3)×O(2)矩阵Ginzburg-Landau-Wilson模型描述的有效场论和非微扰重整化群方法，我们研究了量子涨落和热涨落如何影响参数区的长波行为，其中系统表现出涨落驱动的一阶长程有序跃迁。结果表明，在有限的温度下，从量子Φ^6理论到重整化的二维经典非线性Sigma模型区域出现了交叉，在这个交叉区域中，无质量涨落模和线性色散自旋波支配着低能物理.我们的结果与最近对二维三角海森堡自旋系统NiGa2S4的实验观测结果部分一致.

Study on low-energy properties of two-dimensional quantum triangular Heisenberg modelRecently, Shimizu et al. reported that in an organic Mott insulator with spin $s=1/2$ on a triangular lattice, κ-(ET)2Cu2(CN)3, no magnetic LRO is observed down to 32 mK. Their experimental results suggest the possibility of a new kind of a ground state including the spin liquid. Subsequently, Nakatsuji et al. found that in a quasi-2D quantum triangular HAF with $s=1$, NiGa2S4, there is no sign of LRO down to 0.35 K, in spite of the existence of strong anferromagnetic interactions. In the latter system, the specific heat coefficient C shows the quadratic-temperature dependence at sufficiently low temperatures, and the uniform spin susceptibility is constant in the low temperature regions, indicating the existence of low-lying massless excitations. The origin of these unexpected low-temperature behaviors has not yet been explained.Motivated by these experimental results, we have explored low temperature properties of quantum triangular Heisenberg antiferromagnets in two dimension in the vicinity of the quantum phase transition at zero temperature. Using the effective field theory described by the O(3)×O(2) matrix Ginzburg-Landau-Wilson model and the non-perturbative renormalization group method, we chave larified how quantum and thermal fluctuations affect long-wavelength behaviors in the parameter region where the systems exhibit a fluctuation-driven first order transition to a long-range ordered state. We have shown that at finite temperatures the crossover from a quantum Φ^6 theory to a renormalized two-dimensional classical nonlinear sigma model region appears, and in this crossover region, massless fluctuation modes with linear dispersion spin waves govern low-energy physics.Our results are partly in good agreement with the recent experimental observations for the two-dimensional triangular Heisenberg spin system, NiGa2S4.