论文标题
减少标志问题附近$ t = 0 $ in量子蒙特卡洛模拟
Reduction of the sign problem near $T=0$ in quantum Monte Carlo simulations
论文作者
论文摘要
建立在最近对Shastry-Sutherland模型的调查的基础上[S. Wessel等人，物理。 Rev. B 98，174432（2018）]，我们制定了一种一般策略，以消除沮丧的量子自旋模型中零温度限制附近的蒙特卡洛标志问题。如果利益的哈密顿量和无标志性的哈密顿量（通过在给定的基础上使所有非对角线元件负阴性而获得），则具有相同的基础状态，并且该状态是计算基础的成员，那么随着温度为零，平均符号返回一个。我们通过在饱和度上方的磁场中研究三角形和kagome晶格抗铁磁铁，以及在二聚体基础上修改的husimi仙人掌上的三角形和kagome晶格抗铁磁场来说明这一技术。我们还提供了有关使用线性编程技术自动在量子蒙特卡洛模拟中自动生成有效的有向循环更新的详细附录。
Building on a recent investigation of the Shastry-Sutherland model [S. Wessel et al., Phys. Rev. B 98, 174432 (2018)], we develop a general strategy to eliminate the Monte Carlo sign problem near the zero temperature limit in frustrated quantum spin models. If the Hamiltonian of interest and the sign-problem-free Hamiltonian---obtained by making all off-diagonal elements negative in a given basis---have the same ground state and this state is a member of the computational basis, then the average sign returns to one as the temperature goes to zero. We illustrate this technique by studying the triangular and kagome lattice Heisenberg antiferrromagnet in a magnetic field above saturation, as well as the Heisenberg antiferromagnet on a modified Husimi cactus in the dimer basis. We also provide detailed appendices on using linear programming techniques to automatically generate efficient directed loop updates in quantum Monte Carlo simulations.
