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Physical review. B, Condensed matter

Application of the coupled-cluster method to the periodic Anderson model

Yu Zhou, Alexander J. Majewski, Janice D. Prie, Vassilios Fessatidis, Jay D. Mancini, P. F. Meier

Published Feb 15, 1995• 6 citations
Publisher

Abstract

The coupled-cluster method (CCM) is applied in obtaining the ground-state energy and the local moments of the localized orbitals of the periodic Anderson model. Starting with the state containing a filled Fermi sea of the conduction electrons plus a set of singly occupied and antiferromagnetically ordered f orbitals, the first-order hybridization from the f orbitals to the conduction band is included in the CCM transformation operator. A simple expression for the ground-state energy has been derived, and the calculated ground-state properties are compared with those obtained using a variational scheme and the Monte Carlo method.

DOI
10.1103/physrevb.51.4128

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The coupled-cluster method (CCM) is applied in obtaining the ground-state energy and the local moments of the localized orbitals of the periodic Anderson model. Starting with the state containing a filled Fermi sea of the conduction electrons plus a set of singly occupied and antiferromagnetically ordered f orbitals, the first-order hybridization from the f orbitals to the conduction band is included in the CCM transformation operator. A simple expression for the ground-state energy has been derived, and the calculated ground-state properties are compared with those obtained using a variational scheme and the Monte Carlo method.
The ground-state energy, wave-function, hybridization gap and magnetic phasediagram of the Single Site Impurity Anderson Model (SIAM) and the Periodic AndersonModel (PAM) were calculated using Exact-Diagonalization (ED) technique. The EDtechnique was applied to the SIAM and PAM in one dimension before speculating on Ce 4fbeing a test bed of the results, since it has 4f localized electrons in the Heavy fermioncompound CeCu2Si2. Each of the results obtained describe the evolution of the electronicsystem in terms of a simple set of parameters.The parameter regimes studied suggest asmooth phase transition from an antiferromagnetic (AFM) phase to a ferromagnetic (FM)phase at quarter fillings in one dimension when t increases and a magnetic instability wasobserved as U → ∞. The role of hybridization between the conduction electrons and thelocalized f orbital in the Anderson impurity in a semiconductor was also investigated as Vincreases in the SIAM and the PAM.
The coupled cluster method (CCM) has previously been applied to study the ground- and excited-state properties of many different types of frustrated and unfrustrated quantum spin systems. A common feature in the application of the CCM is to rotate the local spin axes of the (often classical) model state so that (notationally only) the spins all appear to point in the downwards zzz-direction. Hitherto, we remark that only coplanar model states have been used because they do not lead to imaginary terms in the new Hamiltonian. By contrast, non-coplanar "three-dimensional" (3D) model states can lead to imaginary terms in the new Hamiltonian after rotation. In principle, however, macroscopic quantities predicted by the CCM (such as the ground-state energy and order parameter) should still be real (even though the Hamiltonian may be complex) because the transformations of local spin axes are unitary. Here we explain how we may use such 3D model states for the CCM and how we may solve for the (now possibly complex) CCM correlation coefficients. We present results for the spin-half triangular-lattice antiferromagnet in an external magnetic field. We use both coplanar model states and a single 3D non-coplanar model state. We calculate the ground-state energy and the lattice magnetisation as a function of the magnetic field strength. We find that the energies of the coplanar states lie lower than that of the non-coplanar state for all values of the external field, as seen in other approximate studies for this model. We find that the non-coplanar state does not detect the well-known spin plateau occurring in this model, although (as seen before) it is clearly observed for the coplanar model states using the CCM. These results are an excellent initial validation of the new approach for the application of the CCM using 3D model states.
We present a coupled cluster method (CCM) with optimized excitation operators. The efficiency comes from a parameterized form of excitation operators. The parameters are found by variational optimization procedure. The resultant number of excitation operators is much smaller than that of the conventional CCM theory. This property makes it possible to apply the method in systems of solid state physics. Starting from Hartree-Fock state as the reference state, i.e., the Fermi sea, we search for particle-hole excitation operators such that the wave function of configuration interaction in terms of these excitation operators spans a good approximation to the ground state. The Match-pursuit algorithm is capable of doing the search of the excitation operators. The resultant operators are our excitation operators for the CCM wave function. We test the method by two dimensional fermionic Hubbard model on a square lattice.
We have studied electron correlations in the doped two-dimensional (2D) Hubbard model by using the coupled-cluster method (CCM) to investigate whether or not the method can be applied to correct the independent particle approximations actually used in ab initio band calculations. The double excitation version of the CCM, implemented using the approximate coupled pair (ACP) method, accounts for most of the correlation energies of the 2D Hubbard model in the weak $(U/t\ensuremath{\simeq}1)$ and the intermediate U/tU/tU/t regions $(U/t\ensuremath{\simeq}4).$ The error in this case is always less than 11%.1 The ACP approximation gets less accurate for large U/tU/tU/t $(U/t\ensuremath{\simeq}8)$ and near half-filling. Further incorporation of electron correlation effects is necessary in this region. The accuracy depends neither on the system size, nor the gap between the lowest unoccupied level and the highest occupied level in the finite size effect. Hence, the CCM may be favorably applied to ab initio band calculations on metals as well as semiconductors and insulators.
We investigate an extended version of the periodic Anderson model (the so-called periodic Anderson-Hubbard model) with the aim to understand the role of interaction between conduction electrons in the formation of the heavy-fermion and mixed-valence states. Two methods are used: (i) variational calculation with the Gutzwiller wave function optimizing numerically the ground-state energy and (ii) exact diagonalization of the Hamiltonian for short chains. The fff-level occupancy and the renormalization factor of the quasiparticles are calculated as a function of the energy of the fff orbital for a wide range of the interaction parameters. The results obtained by the two methods are in reasonably good agreement for the periodic Anderson model. The agreement is maintained even when the interaction between band electrons, Ud{U}_{d}Ud​, is taken into account, except for the half-filled case. This discrepancy can be explained by the difference between the physics of the one- and higher-dimensional models. We find that this interaction shifts and widens the energy range of the bare fff level, where heavy-fermion behavior can be observed. For large-enough Ud{U}_{d}Ud​ this range may lie even above the bare conduction band. The Gutzwiller method indicates a robust transition from Kondo insulator to Mott insulator in the half-filled model, while Ud{U}_{d}Ud​ enhances the quasiparticle mass when the filling is close to half filling.