Mitigating the Sign Problem through Basis Rotations

Quantum Monte Carlo simulations of quantum many body systems are plagued by the Fermion sign problem. The computational complexity simulating Fermions scales exponentially in projection time $\beta$ and system size. problem is basis dependent an improved basis, for fixed errors, lead to quicker simulations. We show how use sign-free optimize over choice on large two-dimensional systems. numerically illustrate these techniques decreasing `badness' optimizing single-particle rotations one Hubbard find a generic rotation which improves average model wide range $U$ densities $L \times 4$ In example improvement, (and hence simulation cost at accuracy) $16\times $U/t=4$ $n=0.75$ increases $\exp\left[8.64(6)\beta\right]$. For typical times $\beta\gtrapprox 100$, this accelerates such orders magnitude.