Theoretical Study Of Kondo Lattice Model

The heavy fermion material attracts a wide range of attention because of its singu-lar physical properties.The Kondo lattice model(KLM)is one of the most successful theoretical models for the study of heavy fermion materials.The competition,between the Kondo sreening and the RKKY interaction determines the physical properties of the system,and the former tends to form a Kondo singlet at a strong coupling limit,while the latter tends to stabilize a magnetic order in the weakly coupled limit Due to the peculiar linear density of states near the Dirac point,we intend to study the half-filled Kondo lattice model on a honeycomb lattice.We start from the perspective of the mean field and find that with the change of J,the disappearance of the antiferromagnetic order parameter and the occurreence of the Kondo screening occur simultaneously,which is a discontinuous first order transi-tion.But the mean field ignores the quantum fluctuations,although it useful to provide possible orders.Here we intend to go beyond mean field theory from the perspective of variational Monte Carlo(VMC)and dynamical mean-field theory(DMFT).We first simulate a 2 × 2 cells and compare it with exactly diagonalization results and find that the results are similar.We continue to study at a larger lattice,on 6 × 6 cells,we found that with the increase of J,the antiferromagnetic order decrease to 0 with a second order transition and Kondo hybridization also exists in the magnetic region.Finally,we use the DMFT to study at finite temperature.We use the continuous-time quantum Monte Carlo as an impurity solver.We carried out the calculations at various tempera-tures,and finally obtained the phase diagram of the T-J parameter space.there are three different phases:paramagnetic phase,antiferromagnetic phase,Kondo insulator phase.