  In this paper, we discover a new quantum Monte Carlo (QMC) method to solve
the fermion sign problem in interacting fermion models by employing Majorana
representation of complex fermions. We call it "Majorana QMC" (MQMC).
Especially, MQMC is fermion sign free in simulating a class of spinless fermion
models on bipartite lattices at half filling and with arbitrary range of
(unfrustrated) interactions. To the best of our knowledge, MQMC is the first
auxiliary field QMC method to solve fermion sign problem in spinless (more
generally, odd number of species) fermion models. MQMC simulations can be
performed efficiently both at finite and zero temperatures. We believe that
MQMC could pave a new avenue to solve fermion sign problem in more generic
fermionic models.
