Application Of Tensor-Network Methods In Heavy-Fermion Physics

The heavy-fermion system is an important strongly correlated electron system.Competition between Kondo screening and its induced long-range spin interactions con-stitutes the basis of heavy-fermion physics.There are rich physical phenomena in heavy-fermion materials,such as various magnetic orders,unconventional superconductivity,quantum criticality,non-Fermi liquid,hidden order,small to large Fermi surface transi-tion,etc.Further more,the heavy-fermion system is easily tuned by magnetic field,pres-sure,doping,temperature,etc.,making it an important platform to study strongly corre-lated electron systems.The recent experiments that discovered ferromagnetic quantum critical point in the pure heavy-fermion metal CeRh₆Ge₄ and that discovered quantum critical phase in the frustrated heavy-fermion material CePdAl have attracted people to study their related mechanisms and physical phenomena.While inducing rich physical phenomena,strong correlations also pose challenges for theoretical and numerical studies.Analytic methods based on the mean field the-ory or perturbation theory often cannot ensure exact solution and the credibility of the results is difficult to guarantee.And each numerical method has its own limitations,for example,the single-site dynamical mean field theory ignores spatial correlations and quantum Monte Carlo methods may have the negative-sign problem.For the spe-cific research topics,this thesis uses tensor-network methods that can directly handle lattice problems as well as avoiding the negative-sign problem and is one of the im-portant methods to study strongly correlated systems.In tensor-network methods for ground state,the many-body wave function whose dimension grows exponentially with particle numbers is compressed to a tensor network whose dimension has a polynomial growth with particle numbers.The limitation brought by compression is that quantum entanglement of the wave function that can be faithfully represented by a kind of ten-sor network is bounded from above.The matrix product state and projected entangled pair state used in this thesis comply with the area law and volume law of entanglement,and are the commonly used tensor network to study one-and two-dimensional systems,respectively.With tensor network representation,we can obtain the ground state of the many-body system by updating it with variation or imaginary time evolution methods.The first work in this thesis is to study the origin of the continuous ferromagnetic quantum phase transition in heavy-fermion materials with projected entangled pair state and density matrix renormalization group.For the quasi-one-dimensional structure of Cerium atoms in CeRh₆Ge₄,the thesis designs a ferromagnetic Kondo-Heisenberg model with spatial anisotropy in the hopping term and magnetic interaction term,and studies the evolution of the order of ferromagnetic quantum phase transitions with spatial anisotropy with the above two methods.Results show that the ferromagnetic quantum phase transition is continuous in the quasi-one-dimensional limit,but is of first-order in the isotropic limit.Further analysis highlights that the magnetic anisotropy is one im-portant cause leading to the appearance of the continuous ferromagnetic quantum phase transition,which gives a possible explanation to the CeRh₆Ge₄ experiment mentioned above.The second work in this thesis is to study the intermediate phases in the Kondo lattice with density matrix renormalization group.Through careful studies of the one-dimensional frustrated Kondo lattice model with J₁-J₂XXZ interactions among the local moments,the thesis achieves its ground-state phase diagram,from where the pair-density-wave and uniform superconducting states are discovered as intermediate phases.The pair-density-wave state has a small Fermi surface,while the Fermi surface of the uniform superconducting state changes continuously from a partially-enlarged one to a large one with increasing Kondo coupling.The two research works in this thesis have partially explained or further studied the related experiments of CeRh₆Ge₄ and CePdAl,and also provided numerical support for establishment of a complete heavy-fermion ground state theory including ferromag-netism and antiferromagnetism.