Study On Phase Diagram Of Extended Kondo Necklace Model

Investigation of strongly correlated electron systems is the frontier in condensed matter physics.Different from the free Fermi gas,the interaction between electrons dominates the main properties of strongly correlated electron systems,which contain some novel characters and phenomena such as Mott insulator,Kondo insulator,high-temperature superconductor and strange quantum phase transition.In order to understanding the rich physics of strongly correlated systems,condensed matter physicists have presented lots of effective models and methods,which have achieved great success.As the typical topic in strongly correlated electron systems,heavy Fermion systems have been widely investigated in the past years.It is regarded that periodic Anderson model or Kondo lattice model can catch the main physics of heavy Fermion systems.Our work in this thesis are based on the Kondo lattice model,which was presented by Schrieffer and Wolff in 1966 and later attracted great attention.Researches show that a competition between Kondo screening and anti-ferromagnetic interaction which lead to the so-called Doniach phase diagram.Then it is found that the phase transition from Kondo state to anti-ferromagnetic state was a second order quantum phase transition.Based on these research,we focus on the Kondo necklace model which is a good simplified version and retains main physical properties of the Kondo lattice.Using the mean field method,we obtain the ground state phase diagram in accordance with the result of Monte Carlo exactly.So,Kondo necklace model is widely used in dealing with heavy Fermion systems.On this basis,we extend the Kondo necklace model by adding Heisenberg exchange interaction,Ising or Ising-like interaction.Influence of these additional interaction on the ground state phase diagram,especially on the quantum critical point,is studied.We try to apply two kind of mean field methods to study standard Kondo necklace model.One is bond-operator mean field method and another is slave boson mean field method.As a comparison,we find that the former is not applicable and the latter gives reliable results.Therefore,we use bond operator to deal with these extended Kondo necklace models and get their ground state phase diagrams.Comparing with the original phase diagram,we find the Kondo screening region is shrunk in the Kondo necklace-Heisenberg model which indicates that Heisenberg exchange interaction can strengthen anti-ferromagnetic interaction.We find that the Kondo effect region is independent of Ising coupling parameter(JH),the anti-ferromagnetic region moves towards to the area of bigger t/J(t is the the hopping constant of conduction electrons;J is the Kondo coupling constant)in Kodo necklace Ising model.The underlying physics is not clear and further research is needed.We also find the kondo effect region is shrunk when we adding Ising-like interaction to Kondo necklace model.Studies of these extended models deepen our understanding on the quantum spin chain problem and the competitive mechanism between Kondo screening and anti-ferromagnetic interaction in Kondo lattice.These results maybe useful to deal with more complex Kondo lattice.