The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC)

Kaoru Ohno, Keivan Esfarjani, Yoshiyuki Kawazoe

Ma, Xiaoyao

A Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ground state energies for H2O, N2 and F2 molecules. This method has two stages. The first (learning stage) reduces the minus sign problem by optimizing the states which are used in the second (QMC stage). I test the method in Single, Double excitations (SD), Single, Double, and Triple excitations (SDT), and Full Configuration Interaction (FCI) vector spaces. I also perform exact diagonalization in those vector spaces as a benchmark. In each vector space and for each molecule, I perform SiLK QMC for different bond lengths demonstrating that the SiLK QMC is applicable to many systems.

Xiaoyao Ma, Randall W. Hall, Frank Löffler +4 more

The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initio ground state energies for multiple geometries of the H2O, N2, and F2 molecules. The method is based on Feynman's path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of other quantum chemical methods and to exact diagonalization. Our findings demonstrate that the SiLK method is accurate and reduces or eliminates the minus sign problem.

Kaoru Ohno, Keivan Esfarjani, Yoshiyuki Kawazoe

Gaopei Pan, Zi Yang Meng

Sign problem in quantum Monte Carlo (QMC) simulation appears to be an extremely hard yet interesting problem. In this article, we present a pedagogical overview on the origin of the sign problem in various quantum Monte Carlo simulation techniques, ranging from the world-line and stochastic series expansion Monte Carlo for boson and spin systems to the determinant and momentum-space quantum Monte Carlo for interacting fermions. We point out the basis dependency of the sign problem and summarize the progresses to cure, ease and even make use of the sign problem over the years, such as symmetry analysis of the underlying Hamiltonian, basis optimization in writting down the partition functions and many others. Moreover, we state that although traditional lore saying that in case of sign problem, the average sign in QMC simulation approaches zero exponentially fast with the space-time volume of the configurational space, there are recent breakthroughs showing this is not always the case and based on the properties of the partition function for finite size systems, one could distinguish when the average sign has the usual exponential scaling and when it is bestowed with an algebraic scaling at the low temperature limit. Fermionic QMC simulations with such algebraic sign problems have been successfully carried out for extended Hubbard-type and quantum Moiré lattice models.

Mohsen Doust Mohammadi