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Register a new userGround-state properties of the symmetric single-impurity Anderson model on a ring from Density-Matrix Renormalization Group, Hartree-Fock, and Gutzwiller theory
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We analyze the ground-state energy, magnetization, magnetic susceptibility, and Kondo screening cloud of the symmetric single-impurity Anderson model (SIAM) that is characterized by the band width $W$, the impurity interaction strength $U$, and the local hybridization $V$. We compare Gutzwiller variational and magnetic Hartree-Fock results in the thermodynamic limit with numerically exact data from the Density-Matrix Renormalization Group (DMRG) method on large rings. To improve the DMRG performance, we use a canonical transformation to map the SIAM onto a chain with half the system size and open boundary conditions. We compare to Bethe-Ansatz results for the ground-state energy, magnetization, and spin susceptibility that become exact in the wide-band limit. Our detailed comparison shows that the field-theoretical description is applicable to the SIAM on a ring for a broad parameter range. Hartree-Fock theory gives an excellent ground-state energy and local moment for intermediate and strong interactions. However, it lacks spin fluctuations and thus cannot screen the impurity spin. The Gutzwiller variational energy bound becomes very poor for large interactions because it does not describe properly the charge fluctuations. Nevertheless, the Gutzwiller approach provides a qualitatively correct description of the zero-field susceptibility and the Kondo screening cloud. The DMRG provides excellent data for the ground-state energy and the magnetization for finite external fields. At strong interactions, finite-size effects make it extremely difficult to recover the exponentially large zero-field susceptibility and the mesoscopically large Kondo screening cloud.
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We have proposed a density-matrix renormalization group (DMRG) scheme to optimize the one-electron basis states of molecules. It improves significantly the accuracy and efficiency of the DMRG in the study of quantum chemistry or other many-fermion system with nonlocal interactions. For a water molecule, we find that the ground state energy obtained by the DMRG with only 61 optimized orbitals already reaches the accuracy of best quantum Monte Carlo calculation with 92 orbitals.
The density matrix renormalization group method is applied to obtain the ground state phase diagram of the single impurity Anderson model on the honeycomb lattice at half filling. The calculation of local static quantities shows that the phase diagram contains two distinct phases, the local moment (LM) phase and the asymmetric strong coupling (ASC) phase. These results are supported by the local spin and charge excitation spectra, which exhibit qualitatively different behavior in these two phases and also reveal the existence of the valence fluctuating point at the phase boundary. For comparison, we also study the low-energy effective pseudogap Anderson model. Although the high-energy excitations are obviously different, we find that the ground state phase diagram and the asymptotically low-energy excitations are in good quantitative agreement with those for the single impurity Anderson model on the honeycomb lattice, thus providing the first quantitative justification for the previous studies based on low-energy approximate approaches. Furthermore, we find that the lowest entanglement level is doubly degenerate for the LM phase, whereas it is singlet for the ASC phase and is accidentally three fold degenerate at the valence fluctuating point. Our results therefore clearly demonstrate that the low-lying entanglement spectrum can be used to determine with high accuracy the phase boundary of the impurity quantum phase transition.
Using the Bethe ansatz method, we study the ground state properties of a $Utoinfty$ Anderson impurity in a ``gapless host, where a density of band states vanishes at the Fermi level $epsilon_F$ as $|epsilon-epsilon_F|$. As in metals, the impurity spin is proven to be screened at arbitrary parameters of the system. However, the impurity occupancy as a function of the bare impurity energy is shown to acquire novel qualitative features which demonstrate a nonuniversal behavior of the system. The latter explains why the Kondo screening is absent (or exists only at quite a large electron-impurity coupling) in earlier studies based on scaling arguments.
Two-dimensional density-matrix renormalization group method is employed to examine the ground state phase diagram of the Hubbard model on the triangular lattice at half filling. The calculation reveals two discontinuities in the double occupancy with increasing the repulsive Hubbard interaction U at Uc1 = 7.55 t and Uc2 = 9.65 t (t being the hopping integral), indicating that there are three phases separated by first order transitions. The absence of any singularity in physical quantities for 0 < U < Uc1 implies that this phase corresponds to a metallic phase. The local spin density induced by an applied pinning magnetic field for U > Uc2 exhibits a three sublattice feature, which is compatible with the Neel ordered state realized in the strong coupling limit. For Uc1 < U < Uc2, a response to the applied pinning magnetic field is comparable to that in the metallic phase but a relatively large spin correlation length is found with neither valence bond nor chiral magnetic order, suggesting a paramagnetic nature which resembles gapless spin liquid. The calculation also finds that the pair- ing correlation function monotonically decreases with increasing U and thus the superconductivity is unlikely in the intermediate phase.
We investigate the effect of the Coulomb interaction, $U_{cf}$, between the conduction and f electrons in the periodic Anderson model using the density-matrix renormalization-group algorithm. We calculate the excitation spectrum of the half-filled symmetric model with an emphasis on the spin and charge excitations. In the one-dimensional version of the model it is found that the spin gap is smaller than the charge gap below a certain value of $U_{cf}$ and the reversed inequality is valid for stronger $U_{cf}$. This behavior is also verified by the behavior of the spin and density correlation functions. We also perform a quantum information analysis of the model and determine the entanglement map of the f and conduction electrons. It is revealed that for a certain $U_{cf}$ the ground state is dominated by the configuration in which the conduction and f electrons are strongly entangled, and the ground state is almost a product state. For larger $U_{cf}$ the sites are occupied alternatingly dominantly by two f electrons or by two conduction electrons.
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