Weber John L, Vuong Hung, Friesner Richard A, Reichman David R
Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States.
J Chem Theory Comput. 2023 Nov 14;19(21):7567-7576. doi: 10.1021/acs.jctc.3c00654. Epub 2023 Oct 27.
We formulate and characterize a new constraint for auxiliary-field quantum Monte Carlo (AFQMC) applicable for general fermionic systems, which allows for the accumulation of phase in the random walk but disallows walkers with a magnitude of phase greater than π with respect to the trial wave function. For short imaginary times, before walkers accumulate sizable phase values, this approach is equivalent to exact free projection, allowing one to observe the accumulation of bias associated with the constraint and thus estimate its magnitude . We demonstrate the stability of this constraint over arbitrary imaginary times and system sizes, highlighting the removal of noise due to the fermionic sign problem. Benchmark total energies for a variety of weakly and strongly correlated molecular systems reveal a distinct bias with respect to standard phaseless AFQMC, with a comparative increase in accuracy given sufficient quality of the trial wave function for the set of studied cases. We then take this constraint, termed linecut AFQMC (lc-AFQMC), and systematically release it (lcR-AFQMC), providing a route to obtain a smooth bridge between constrained AFQMC and the exact free projection results.
我们为适用于一般费米子系统的辅助场量子蒙特卡罗（AFQMC）制定并描述了一种新的约束条件，该条件允许在随机游走中积累相位，但不允许相对于试探波函数相位大小大于π的游走者。对于短虚时间，在游走者积累可观的相位值之前，这种方法等同于精确自由投影，从而能够观察到与该约束相关的偏差积累，进而估计其大小。我们展示了这种约束在任意虚时间和系统规模上的稳定性，突出了由于费米子符号问题导致的噪声消除。对各种弱关联和强关联分子系统的基准总能量表明，相对于标准无相位AFQMC存在明显偏差，在所研究的案例集中，若试探波函数质量足够，则精度会有相应提高。然后，我们采用这种被称为线切割AFQMC（lc - AFQMC）的约束条件，并系统地放松它（lcR - AFQMC），提供了一条在约束AFQMC和精确自由投影结果之间获得平滑过渡的途径。
