Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
J Chem Phys. 2013 Jan 14;138(2):024110. doi: 10.1063/1.4773819.
The sign problem in full configuration interaction quantum Monte Carlo (FCIQMC) without annihilation can be understood as an instability of the psi-particle population to the ground state of the matrix obtained by making all off-diagonal elements of the Hamiltonian negative. Such a matrix, and hence the sign problem, is basis dependent. In this paper, we discuss the properties of a physically important basis choice: first versus second quantization. For a given choice of single-particle orbitals, we identify the conditions under which the fermion sign problem in the second quantized basis of antisymmetric Slater determinants is identical to the sign problem in the first quantized basis of unsymmetrized Hartree products. We also show that, when the two differ, the fermion sign problem is always less severe in the second quantized basis. This supports the idea that FCIQMC, even in the absence of annihilation, improves the sign problem relative to first quantized methods. Finally, we point out some theoretically interesting classes of Hamiltonians where first and second quantized sign problems differ, and others where they do not.
无消去的完全组态相互作用量子蒙特卡罗（FCIQMC）中的符号问题可以理解为，在将哈密顿量的所有非对角元素置负后，psi 粒子种群对矩阵基态的不稳定性。这样的矩阵，以及因此的符号问题，是基依赖的。在本文中，我们讨论了一种物理上重要的基选择的性质：第一性和第二性。对于给定的单粒子轨道选择，我们确定了在反对称 Slater 行列式的第二量子化基中费米子符号问题与非对称 Hartree 乘积的第一量子化基中符号问题相同的条件。我们还表明，当两者不同时，费米子符号问题在第二量子化基中总是更不严重。这支持了 FCIQMC（即使没有消去）相对于第一量子化方法改善符号问题的观点。最后，我们指出了一些在理论上有趣的 Hamilton 量类，其中第一性和第二性量子化的符号问题不同，而其他 Hamilton 量类则没有。
