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On metal–insulator transition for a one-dimensional correlated nanoscopic chain

Rycerz, Adam, Józef Spałek

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

We have applied our novel numerical scheme combining Lanczos diagonalization in the Fock space with an ab initio renormalization of the single-particle (Wannier) functions, to study the ground state properties of the Extended Hubbard Model. Through the finite-size scaling we determine the discontinuity of the momentum distribution Fermi surface. Our results imply Fermi-liquid behavior for lattice parameter a $\lesssim$ 3a$_{0}$ (a$_{0}$ is the Bohr radius) and zero-temperature transition to the localized spin system for larger . Possible further applications of the method are listed at the end.

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AIP conference proceedings•Jan 1, 2002•0 citations
We have applied our novel numerical scheme combining Lanczos diagonalization in the Fock space with an ab initio renormalization of the single-particle (Wannier) functions, to study the ground state properties of the Extended Hubbard Model. Through the finite-size scaling we determine the discontinuity of the momentum distribution Fermi surface. Our results imply Fermi-liquid behavior for lattice parameter a ≲\lesssim≲ 3a0_{0}0​ (a0_{0}0​ is the Bohr radius) and zero-temperature transition to the localized spin system for larger . Possible further applications of the method are listed at the end.
We review our recent results concerning the electronic properties of a nanoscopic system with inclusion of long‐range Coulomb interactions that are obtained by combining exact diagonalization in the Fock space with an ab initio method (EDABI). The system evolution is discussed as a function of lattice parameter R. A transformation from a nanometal to localized spin system is observed. With the help of a finite‐size scaling we determine the discontinuity of the momentum distribution at the Fermi points. Our results imply Fermi‐liquid‐like behavior for R ≲ 3a0 (a0 is the Bohr radius). The quasiparticle mass is almost divergent at the localization threshold, where the particle distribution of the Fermi‐Dirac type gets smeared out. The charge‐gap evolution is compared with that of the Slater gap. Also, the single‐particle spectral function and the corresponding density of states are presented. The analysis is performed using 1s‐like Gaussian‐type STO‐3G basis.
We discuss the physical properties of strongly correlated electron states for a linear chain obtained with the help of a recently proposed method combining an exact diagonalization in Fock space with an ab initio readjustment of single-particle orbitals in the correlated state. The method extends the current discussion of correlated states, since the properties are obtained with varying lattice spacings. The finite system of N atoms evolves with the increasing interatomic distance from a Fermi-liquid-like state into the Mott insulator. The criteria of the localization are discussed in detail, since the results are already convergent for N> 8.N>~8.N> 8. During this process the Fermi-Dirac distribution is smeared out, the effective band mass increases by \ensuremath{\sim}50%, and the spin-spin correlation functions reduce to those for a Heisenberg antiferromagnet. Values of microscopic parameters such as the hopping and the kinetic-exchange integrals, as well as the magnitude of both intraatomic and interatomic Coulomb and exchange interactions are calculated. We also determine the values of various local electron-lattice couplings, and show that they are comparable to the kinetic exchange contribution in the strong-correlation limit. The magnitudes of the dimerization and the zero-point motion are also discussed. Our results provide a canonical example of a tractable strongly correlated system with a precise, first-principles description as a function of interatomic distance of a model system involving all hopping integrals, all pair-site interactions, and exact one-band Wannier functions.
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We consider the Ising phase of the antiferromagnetic XXZ Heisenberg chain on a finite-size lattice with N sites. We compute the large-NNN behavior of the spin stiffness, obtaining the correlation length $\ensuremath{\xi}.$ We use our results to discuss the scaling behavior of the metal-insulator transitions in one-dimensional systems, taking into account the mapping between the XXZ Heisenberg chain and the spinless fermion model, and known results for the Hubbard model. We study the scaling properties of both the Hubbard model and the XXZ Heisenberg chain by solving numerically the Bethe ansatz equations. We find that for some range of values of $\ensuremath{\xi}/N,$ the scaling behavior may be observed for the Hubbard model but not for the XXZ Heisenberg chain. We show how $\ensuremath{\xi}$ can be obtained from the scaling properties of the spin stiffness for small system sizes. This method can be applied to models having not an exact solution, illuminating their transport properties.
We present our new method of approach to the interacting electron systems combining the exact diagonalization of the Hamiltonian in the Fock space (including all hopping integrals and all two‐site interactions) with an ab initio optimization of the single particle (Wannier) functions in the resultant ground state. Such a procedure is applied to the analysis of the electron localization in nanoscopic chains containing up to N = 12 atoms. Electrons are essentially localized for the interatomic distance R > 2.2 Å. The statistical distribution evolves from the Fermi‐liquid limit (at R ∼ 1 − 2 Å) to continuous momentum distribution for R > 2.2 Å. The Mott and the Hubbard criteria of localization are explicitly evaluated and the importance of the former is stressed. Futher applications of our method are listed at the end.