Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
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二维哈伯德模型的解：各种数值算法的基准和结果
DOI：
10.1103/physrevx.5.041041
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发表时间：
2015-12-14
影响因子：
12.5
通讯作者：
Gull, Emanuel
中科院分区：
文献类型：
--
作者：
LeBlanc, J. P. F.;Antipov, Andrey E.;Gull, Emanuel
提出了二维方晶格上单轨道哈伯德模型的基态和激发态性质（能量、双占据和松原轴自能）的数值结果，以便评估我们在热力学极限下计算准确结果的能力。采用了多种方法，包括辅助场量子蒙特卡罗、裸线和粗线图解蒙特卡罗、对偶费米子方法、密度矩阵嵌入理论、密度矩阵重正化群、动态簇近似、固定节点近似内的扩散蒙特卡罗、无限制耦合簇理论和多参考投影Hartree-Fock方法。比较不同方法获得的结果可以识别不确定性和系统误差。强调了外推到收敛热力学极限值的重要性。不同方法之间达成一致的情况建立了基准结果，这些结果可能有助于验证新方法和改进现有方法。
Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.