Perturbative solution of fermionic sign problem in quantum Monte Carlo computations

Abstract

Abstract We have developed a 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 discrete 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-neighbor 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 straightforward lattice QMC calculations. We also discuss the formation of the pseudogap and the nodal-antinodal dichotomy for a doped Hubbard system with the interaction parameter U equal to the bandwidth and the optimal value of the next-nearest-neighbor hopping parameter $${t}^{{\prime} }$$ t ′ for high-temperature superconducting cuprates.