论文标题
2D哈伯德模型的热张量网络模拟的切线空间方法
Tangent Space Approach for Thermal Tensor Network Simulations of the 2D Hubbard Model
论文作者
论文摘要
二维（2D）哈伯德模型的准确模拟构成了凝结物质和量子物理学中最具挑战性的问题之一。在这里，我们开发了一个切线空间张量重新归一化组（TANTRG）方法，以在有限温度下计算2D哈伯德模型。在Tantrg中以轻度$ O（d^3）$复杂性实现密度运算符的最佳演变，其中债券尺寸$ d $控制着准确性。通过Tantrg方法，我们可以提高大规模2D哈伯德系统的低温计算，最高为宽度8缸和$ 10 \ times10 $ square lattice。对于半填充的哈伯德模型，获得的结果与行列式量子蒙特卡洛（DQMC）的结果非常吻合。此外，Tantrg可用于探索DQMC无法访问的低温，有限兴奋剂的制度。发现计算出的电荷可压缩性和Matsubara Green的功能分别反映了奇怪的金属和伪制作行为。超导配对的易感性被计算为低温约为$ 1/24 $的跳跃能量，我们发现$ d $ - 波配对响应在最佳掺杂量附近最为重要。 Tantrg配备了切线空间技术，构成了一种在有限温度下强烈相关的2D晶状体模型的良好控制，高效且准确的张量网络方法。
Accurate simulations of the two-dimensional (2D) Hubbard model constitute one of the most challenging problems in condensed matter and quantum physics. Here we develop a tangent space tensor renormalization group (tanTRG) approach for the calculations of the 2D Hubbard model at finite temperature. An optimal evolution of the density operator is achieved in tanTRG with a mild $O(D^3)$ complexity, where the bond dimension $D$ controls the accuracy. With the tanTRG approach we boost the low-temperature calculations of large-scale 2D Hubbard systems on up to a width-8 cylinder and $10\times10$ square lattice. For the half-filled Hubbard model, the obtained results are in excellent agreement with those of determinant quantum Monte Carlo (DQMC). Moreover, tanTRG can be used to explore the low-temperature, finite-doping regime inaccessible for DQMC. The calculated charge compressibility and Matsubara Green's function are found to reflect the strange metal and pseudogap behaviors, respectively. The superconductive pairing susceptibility is computed down to a low temperature of approximately $1/24$ of the hopping energy, where we find $d$-wave pairing responses are most significant near the optimal doping. Equipped with the tangent-space technique, tanTRG constitutes a well-controlled, highly efficient and accurate tensor network method for strongly correlated 2D lattice models at finite temperature.
