Study of spin fluctuations, and superconductivity and superfluidity in two dimensional fermion systems

Abstract

The wave number dependence of the susceptibility can be the most important factor determining the symmetry of the Cooper pair in two dimensional superfluid 3He. The correlation effects on the wave number dependence of the susceptibility in two-dimensional fermion systems were studied by a simple second order perturbation theory. The Quantum Monte Carlo (QMC) calculations on a two-dimensional Hubbard model were employed to examine strong correlation effects on the wave number dependence of the susceptibility. The static susceptibility in the dilute Hubbard model was obtained by Fluctuation-Exchange approximation (FLEX) as a function of wave number. The non-analyticity was not observed in the QMC results nor in the FLEX results, presumably because the calculations were performed on lattices of finite size and were not performed at very low temperatures. Effective interaction between quasiparticles mediated by spin fluctuations was estimated by using a paramagnon theory.

磁化率の波数依存性は2次元超流体3Heにおけるクーパー対の対称性の決定に最も重要な要素である。2次元フェルミ粒子系における磁化率の波数依存性の相関効果を簡単な2次摂動理論を用いて研究した。磁化率の波数依存性における強相関効果を調べるために2次元ハバード模型において量子モンテカルロ(QMC)計算を用いた。ゆらぎ交換近似(FLEX)により得られた希薄ハバード模型中の静磁化率を波数の関数として示した。非解析性はQMC計算結果にもFLEX計算結果にも観測されなかった。これは恐らく、計算が有限サイズの格子で実行されたためと低い温度で実行されなかったためであると考えられる。さらに、スピンゆらぎを介した準粒子間の相互作用をパラマグノン理論により推定した。