Rost D, Assaad F, Blümer N
Institute of Physics, Johannes Gutenberg University, Mainz, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 May;87(5):053305. doi: 10.1103/PhysRevE.87.053305. Epub 2013 May 29.
We present an algorithm for solving the self-consistency equations of the dynamical mean-field theory (DMFT) with high precision and efficiency at low temperatures. In each DMFT iteration, the impurity problem is mapped to an auxiliary Hamiltonian, for which the Green function is computed by combining determinantal quantum Monte Carlo (BSS-QMC) calculations with a multigrid extrapolation procedure. The method is numerically exact, i.e., yields results which are free of significant Trotter errors, but retains the BSS advantage, compared to direct QMC impurity solvers, of linear (instead of cubic) scaling with the inverse temperature. The new algorithm is applied to the half-filled Hubbard model close to the Mott transition; detailed comparisons with exact diagonalization, Hirsch-Fye QMC, and continuous-time QMC are provided.
我们提出了一种算法，用于在低温下高精度、高效率地求解动态平均场理论（DMFT）的自洽方程。在每次DMFT迭代中，杂质问题被映射到一个辅助哈密顿量，其格林函数通过将行列式量子蒙特卡罗（BSS-QMC）计算与多重网格外推程序相结合来计算。该方法在数值上是精确的，即产生的结果没有显著的 Trotter 误差，但与直接的QMC杂质求解器相比，保留了BSS的优势，即与逆温度呈线性（而非立方）标度关系。新算法被应用于接近莫特转变的半填充哈伯德模型；提供了与精确对角化、赫希 - 菲耶QMC和连续时间QMC的详细比较。
