EMUS-QMC: Elective Momentum Ultra-Size Quantum Monte Carlo Method

One bottleneck of quantum Monte Carlo (QMC) simulation of strongly correlated electron systems lies at the scaling relation of computational complexity with respect to the system sizes. For generic lattice models of interacting fermions, the best methodology at hand still scales with $beta N^3$ where $beta$ is the inverse temperature and $N$ is the system size. Such scaling behavior has greatly hampered the accessibility of the universal infrared (IR) physics of many interesting correlated electron models at (2+1)D, let alone (3+1)D. To reduce the computational complexity, we develop a new QMC method with inhomogeneous momentum-space mesh, dubbed elective momentum ultra-size quantum Monte Carlo (EQMC) method. Instead of treating all fermionic excitations on an equal footing as in conventional QMC methods, by converting the fermion determinant into the momentum space, our method focuses on fermion modes that are directly associated with low-energy (IR) physics in the vicinity of the so-called hot-spots, while other fermion modes irrelevant for universal properties are ignored. As shown in the manuscript, for any cutoff-independent quantities, e.g. scaling exponents, this method can achieve the same level of accuracy with orders of magnitude increase in computational efficiency. We demonstrate this method with a model of antiferromagnetic itinerant quantum critical point, realized via coupling itinerant fermions with a frustrated transverse-field Ising model on a triangle lattice. The system size of $48 times 48 times 32$ ($Ltimes Ltimesbeta$, almost 3 times of previous investigations) are comfortably accessed with EQMC. With much larger system sizes, the scaling exponents are unveiled with unprecedentedly high accuracy, and this result sheds new light on the open debate about the nature and the universality class of itinerant quantum critical points.