Quantum Monte Carlo(QMC) is one of the most powerful and successful methods to simulate many-body systems. Unfortunately, there is always a notorious problem called “Sign Problem”, especially in fermion systems or frustrated spin models. And the solution of the Sign Problem is considered to be nondeterministic polynomial (NP) hard[1]. In this talk, I will briefly introduce the definition of Sign Problem, some explanations of its origin[2], and some ideas for trying to solve it[3,4,5]. I will try to avoid going into too much detail and hope to explain the ideas as much as possible.

[1] Matthias Troyer et al.  Phys. Rev. Lett. 94, 170201(2005)

[2] Mauro Iazzi et al.     Phys. Rev. B 93, 115102 (2016)

[3] Congjun Wu et al.    Phys. Rev. B 71, 155115 (2005)

[4] Lei Wang et al.       Phys. Rev. Lett. 115, 250601 (2015)

[5] Z. C. Wei et al.       Phys. Rev. Lett. 116, 250601 (2016)