Preconditioning the Quantum Many-Body Problem

Modern algorithmic developments in Lattice Monte Carlo calculations, collectively referred to as Hybrid Monte Carlo (HMC), have dramatically improved the computational scaling of many-fermion simulations for large system volumes $V$. From the conventional $V^3$ or $V^2$ laws, we now know it is possible to reach $V^\alpha$ scaling with $\alpha\simeq 1.25$. However, the overall factor of the scaling law could and should be improved. This factor is determined in part by the number of iterations required for the solution of an ill-conditioned linear problem, which is repeatedly performed in HMC. In this contribution we present the results of a number of preconditioning strategies that accelerate and stabilize this linear problem for the case of strongly interacting non-relativistic fermions in $3+1$ dimensions.