Overcoming Fermionic Sign Problem in Quantum Monte Carlo Computations: Reference System Method

Abstract We have developed a novel strong-coupling perturbation scheme for a general doped Hubbard model around a particle-hole-symmetric reference system, which is free from the fermionic sign problem. Our approach is based on the lattice determinantal Quantum Monte Carlo (QMC) method in both continuous and dis- crete time versions for large periodic clusters in a fermionic bath. By considering the first-order perturbation in the shift of the chemical potential and the second- neighbour hopping, we are able to obtain an accurate electronic spectral function for a range of parameters that correspond to optimally doped cuprate systems at temperatures of up to T = 0.1t, which are challenging to access using straightfor- ward lattice QMC calculations. We also discuss the formation of the pseudogap and the nodal-antinodal dichotomy for a doped Hubbard system with the interac- tion parameter U equal to the bandwidth and the optimal value of the next-nearest- neighbor hopping parameter t′ for high-temperature superconducting cuprates.