Determinant Monte Carlo Study Of Antiferromagnetism Metallic Quantum Critical Point

The quantum criticality in strong correlated itinerant electron system,which is considered as origin of many novel phenomena such as the non-Fermi-liquid in heavy fermion compounds and strange metal phase in high temperature superconductors,hold very unique position in the modern condensed matter physics research.A quantum critical point(QCP)of particular interest is found at the zero-temperature onset of spin density wave(SDW)long range order in two-dimensional metals.Due to the complex and non-perturbative nature,these systems belong to the most difficult and challenging problems in the study of modern condensed matter physics,and an in-depth understanding of this quantum criticality universal mechanism still remains highly desirable.Due to the lack of appropriate theoretical descriptions,the efficient quantum many-body numerical methods offer a powerful tool to tackle these types of problem.Quantum Monte Carlo(QMC)methods are unique numerically exact and unbiased method to simulate interacting quantum many-body systems.QMC methods capture the low energy universal physics by solve the lattice model numerically.In recent years,it has becoming clear that many interesting strong correlated model can only be solved by QMC via careful design of sign-problem-free model which capture the these important physics.In particular,the recent developed self-learning Monte Carlo(SLMC)method and momentum space designer model method reduced the heavy matrix computation in fermion system and the sampling problem in quantum critical region(critical slowing down)of fermionic Monte Carlo simulations,which enabled unbiased large-scale numerical simulation to be achieved in the quantum critical region.In these thesis,I focus on investigating one type of the sign-problem-free spin-fermion lattice model in(2+1)dimension with large-scale quantum Monte Carlo method,which describes a quantum spin model coupling to doped Fermi surface.At quantum critical region,the spin anti-ferromagnetic fluctuation strongly interact with low energy fermion excitation and make the universality class of the system drasticly deviating from prediction of pure spin model.Within the Hertz-Millis-Moriya(HMM)theory,mean-field critical exponents shall always be expected in these metallic quantum critical points regardless of microscopic details.However,we found an interesting difference between the 3 = ? and 2 = ? anti-ferromagnetic quantum critical points.Close to quantum critical points,the analysis of spin correlation function shows the former is actually consistent with the HMM prediction and the latter is deviated from the HMM and acquires the finite anomalous dimension.Our results provide the first set of concrete numerical evidence for different types of anti-ferromagnetic quantum critical points depending on the value of anti-ferromagnetic ordering wavevector ,and explicitly demonstrate the exist of quantum criticality beyond the HMM framework.