Alleviating the sign problem in quantum Monte Carlo simulations of spin-orbit-coupled multiorbital Hubbard models
Alleviating the sign problem in quantum Monte Carlo simulations of spin-orbit-coupled multiorbital Hubbard models
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DOI：
10.1103/physrevb.101.045108
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发表时间：
2019-07
影响因子：
3.7
通讯作者：
A. Kim;P. Werner;R. Valent'i
中科院分区：
文献类型：
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作者：
A. Kim;P. Werner;R. Valent'i
提出了一种缓解自旋-轨道耦合多轨道Hubbard模型动力学平均场(DMFT)方程的连续时间量子蒙特卡罗(CTQMC)模拟中的符号问题的策略。我们首先确定了在相对论基中存在的旋转不变的Hund耦合项的组合，这些组合导致了严重的符号问题。利用CTQMC中平均符号依赖于单粒子基的选择这一事实，我们提出了一个成键-反键基函数{V_{J3/2\mathrm{BA}，对于所研究的大多数参数集，它比广泛使用的相对论基有更好的平均符号。然后，我们通过引入一个利用单粒子基空间的随机优化算法来推广这一过程，并证明了在所研究的参数空间内，$V{J3/2\mathm{BA}}$非常接近于最优。我们的发现使得对具有强自旋轨道耦合的材料进行更有效的DMFT模拟。
We present a strategy to alleviate the sign problem in continuous-time quantum Monte Carlo (CTQMC) simulations of the dynamical-mean-field-theory (DMFT) equations for the spin-orbit-coupled multiorbital Hubbard model. We first identify the combinations of rotationally invariant Hund coupling terms present in the relativistic basis which lead to a severe sign problem. Exploiting the fact that the average sign in CTQMC depends on the choice of single-particle basis, we propose a bonding-antibonding basis $V_{j3/2\mathrm{BA}}$ which shows an improved average sign compared to the widely used relativistic basis for most parameter sets investigated. We then generalize this procedure by introducing a stochastic optimization algorithm that exploits the space of single-particle bases and show that $V_{j3/2\mathrm{BA}}$ is very close to optimal within the parameter space investigated. Our findings enable more efficient DMFT simulations of materials with strong spin-orbit coupling.