Geometrical Frustration in Strongly Correlated Electron Systems

二维量子三角海森堡模型的低能性质研究最近，Shimizu等人报道了在三角晶格上自旋为1/2的有机Mott绝缘体κ-（ET）2Cu 2（CN）3中，在低至32 mK时没有观察到磁性LRO。他们的实验结果表明，一种新的基态，包括自旋液体的可能性。随后，Nakatsuji等人发现，在准二维量子三角形HAF中，$s=1$，NiGa 2S 4，尽管存在强的反铁磁相互作用，但在0.35 K以下没有LRO的迹象。在后一个系统中，在足够低的温度下，比热系数C表现出二次温度依赖性，并且均匀自旋极化率在低温区域是恒定的，表明存在低位无质量激发。受这些实验结果的启发，我们研究了二维量子三角海森堡反铁磁体在零温量子相变附近的低温性质。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，我们讨论了量子涨落和热涨落如何影响系统在参数区的长波行为，在参数区，系统表现出涨落驱动的一级跃迁到长程有序态.我们证明了在有限温度下量子Φ^6理论与二维经典非线性sigma模型区域的交叉，在这个交叉区域中，具有线性色散自旋波的无质量涨落模支配着低能物理，我们的结果与最近对二维三角形海森堡自旋系统NiGa 2S 4的实验观察部分一致。

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.