Geometrical Frustration in Strongly Correlated Electron Systems

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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.