在強關聯系統中尋找有趣的新物相及其相變一直是凝體物理中熱門研究的課題，例如在高溫超導體中除了有反鐵磁相、D-波超導相、Pseudo-Gap 相之外，尚有條紋相等。以La2-xBaxCuO4 超導體為例，超導相變溫度Tc 在電洞密度(x)為1/8 時突然降至4K，而x=1/8 也是條紋相最顯著的密度，這似乎意味著條紋相是高溫超導體在眾多交互作用競爭下的一個低能量狀態，可能會因材料的些微差異使超導相被破壞而形成條紋相，甚或有理論認為條紋相的發生不利於超導相的?定，二者互相排斥。然而2007 年，Tranquada 的實驗群指出條在條紋相中仍可測量到2 維的超導性。因此條紋相似乎並不排斥超導，反而是促使2 維超導配對的機制。近兩年來，許多熱烈的研究能量集中在這個議題上面。本計畫主持人將以過去在強關聯系統的研究經驗，嘗試對此課題做一系統化的研究。我們的研究方法是以變分蒙地卡羅法來研究t-J 及Hubbard 模型。變分法是少數能精確處理「非雙佔據」限制的方法，它沒有負號問題，也能研究較大的晶格。雖然此法受到波函數的變分空間的限制，但我們可以結合平均場的計算及物理直觀的考量來加以改善。第一年的工作在釐清t-J 模型是否能預言「超導條紋相」？若否，則需引入何種修正，方可使之存在？第二年的工作則考慮引入Frustration 效應至t-J 模型，此項研究的目的在尋找t-J 模型是否存在超固相，即超導與valence bond 固體共存。第三年的主題是研究雙層強關聯玻色子系統的配對超流體與超固相。 The search of interesting new phases and phase transitions among them in the systems of strongly correlated systems has been a topic of general interests in the field of condensed-matter physics. For instance, anti-ferromagnetism, D-wave superconductivity, pseudo-gap and stripe phases are observed in the high-temperature superconductors. Recently, interesting transport experiments on La1.875Ba0.125CuO4 reveals that there exists two-dimensional superconductivity in the stripe phase with temperature above the set-in of the bulk superconductivity at 4K. Previously the fact of low Tc of this material, which has the robust stripe at 1/8 doping density, has been taken as the evidence that stripe is competing with D-wave superconductivity. Based on the recent results, the theory of stripe superconductivity emphasizes that stripe is not a competing phase for superconductivity but quite on the contrary a helper which provides binding force between pair of holes in the stripe. There are warm discussions of this stripe issue in the recent two years. The principle investigator has years of experiences on the research of strongly correlated systems.We will carry out systematic study of the stripe phase of the t-J and Hubbard models by variational Monte Carlo (VMC) method. VMC can treat the constraint of ‘no double occupancy’exactly, free from the “negative sign problem”and feasible for large lattice calculation. Though the limitation of the variational space makes this approach non-exact, we can verify the physical intuition from theoretical analysis through VMC.We expect improved wave function can be reached by mean-field theory. In the first year, we will determine if stripe superconductivity can be a lowest state in the t-J type models.We will also consider extension of the model Hamiltonian which will predict a stripe superconducting phase. Following the work of 1st year, we will introduce frustration effect into the t-J model.We will perform VMC calculation for the checkerboard lattice to verify the enhanced pairing obtained in the study by exact diagonalization. IN the final year, we will focus on the paired superfluidity and supersolid of the double-layer bosonic systems.
