Fermion sign bounds theory in quantum Monte Carlo simulation

Sign problem in fermion quantum Monte Carlo (QMC) simulation appears to be an extremely hard problem. Traditional lore passing around for years tells people that when there is a sign problem, the average QMC approaches zero exponentially fast with space-time volume of configurational space. We, however, analytically show this not always case and manage find physical bounds sign. Our understanding based on direct connection between well-defined partition function reference system could distinguish have usual exponential scaling, they are bestowed algebraic scaling at low temperature limit. We explain such problems found flat band moir\'e lattice models At finite temperature, domain size argument also explains behavior phase transition. bounds, as observable, may ability ease or even make use