Application Of Determinant Quantum Monte Carlo In Quantum Many-body Physics

Understanding the non-Fermi liquid behavior in condensed matter systems beyond Landau Fermi liquids theory will be of great help in understanding,for example,heavy Fermion systems and strange metal phase in unconventional superconductivity.Since it is difficult to have a general and universal theory to deal with the complex and subtle system called strongly correlated system,it is particularly important to use numerical simulation method to assist us in understanding it.The unbiased quantum Monte Carlo method is one of them.In this paper,we first discuss the numerical simulation of Yukawa-SYK model with self-tuned quantum criticality using quantum Monte Carlo method.For the usual systems with non-fermi liquid behavior,fermions are always coupled with the bosonic system which has quantum phase transition.At this time,there is a bosonic mode in the quantum critical region where there is a coupling between fermions and bosons,so as to make the system behave as non-fermi liquid.This approach has a high precision requirement for finding the quantum critical regions of different models.The Yukawa-SYK model studied by the author et al.randomly coupled the boson and fermion together,so that no matter how much the bare mass of the boson is,the random coupling makes boson gapless,which makes it possible to study its non-Fermi liquid behavior in a large range.In addition,for twisted bilayer graphene systems with rich physics such as unconventional superconducting and topological flat band,we develop momentum-space Monte Carlo methods to numerically simulate a twisted bilayer graphene systems projected onto flat band with long-range screened coulomb interactions.For the charge neutral point,our calculations show that the ground state is likely the Kramer inter-valleycoherent state.At the same time,the dynamical behavior of the (2)ferromagnetic Goldstone mode is observed near the Γ point.In addition,for the filling of =-3,the thermodynamic Ising phase transition is shown in our calculations,and the ground state of it is proved to be a quantum anomalous Hall state by calculating the corresponding order parameters and the Chern number at low temperature.At the same time,the author et al.also developed the sign boundary theory,which is especially suitable for the projected twisted systems,and gave the lower bound of the sign in the zero temperature limit of the system,and proved that for a class of systems,the behaviors of sign are different from the usual exponential decay with the system size,but show the power law decay behavior.