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Ergodicity of the hybridization-expansion Monte Carlo algorithm for broken-symmetry states

机译：破对称状态下杂交扩展蒙特卡罗算法的遍历性

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With the success of dynamical mean-field theories, solvers for quantum-impurity problems have become an important tool for the numerical study of strongly correlated systems. Continuous-time quantum Monte Carlo sampling of the expansion in powers of the hybridization between the "impurity" and the bath provides a powerful solver when interactions are strong. Here we show that the usual updates that add or remove a pair of creation-annihilation operators are rigorously not ergodic for several classes of broken symmetries that involve spatial components. We show that updates with larger numbers of simultaneous updates of pairs of creation-annihilation operators remedy this problem. As an example, we apply the four-operator updates that are necessary for ergodicity to the case of d-wave superconductivity in plaquette dynamical mean-field theory for the one-band Hubbard model. While the results are qualitatively similar to those previously published, they are quantitatively better than previous ones, being closer to those obtained by other approaches.
机译：随着动力学平均场理论的成功，量子杂质问题的求解器已成为进行强相关系统数值研究的重要工具。当相互作用较强时，连续时间量子蒙特卡洛采样法对“杂质”和熔池之间的杂交能力进行了扩展，从而提供了强大的求解器。在这里，我们表明，对于涉及空间分量的几类破坏对称性，添加或删除一对创建an灭运算符的常规更新严格不遍历。我们显示，使用创建-operators灭运算符对的同时更新数量较大的更新可以解决此问题。例如，对于单波段Hubbard模型，在球状动力学平均场理论中，我们将遍历性所需的四运算符更新应用于d波超导的情况。虽然结果在质量上与先前发表的结果相似，但在数量上要比先前的结果更好，更接近于其他方法获得的结果。

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