Benchmarking the accuracy of superconducting pair-pair correlations within Constrained Path Quantum Monte Carlo

Abstract

Ground state properties of the Hubbard model are of fundamental importance to understand the mechanism of unconventional superconductivity in the high-T_c cuprates and other materials. One of the most powerful numerical methods for strongly interacting models is quantum Monte Carlo, which however faces a fundamental limitation, the Fermion sign problem. The sign problem can be mitigated using approximate methods such as Constrained Path Monte Carlo, where the sign of the overlap with a trial wavefunction is constrained to remain positive. Beyond the constraint, additional approximations must be made in order to measure observables for operators that do not commute with the Hamiltonian. We examine critically the most commonly used approximation, back propagation, as well as a recently proposed constraint release measurement technique. In comparisons with a variety of systems that can be solved numerically exactly by other methods, we find that back propagation tends to underestimate long-range superconducting pair-pair correlations. Except in special cases such as one dimension, back propagation introduces an uncontrolled approximation even when the exact trial wavefunction is used. The constraint release technique can provide accurate results, with the disadvantages that it much more computationally expensive and reintroduces the sign problem.

arXiv comment13 pages, 12 figures