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arXiv:cond-mat/0507132 · Physical Review B

Electron spectra close to a metal-to-insulator transition

Michał Karski, Carsten Raas, Götz Silvester Uhrig

Published Sep 27, 2005• 57 citations
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Abstract

A high-resolution investigation of the electron spectra close to the metal-to-insulator transition in dynamic mean-field theory is presented. An all-numerical, consistent confirmation of a smooth transition at zero temperature is provided. In particular, the separation of energy scales is verified. Unexpectedly, sharp peaks at the inner Hubbard band edges occur in the metallic regime. They are signatures of the important interaction between single-particle excitations and collective modes.

DOI
10.1103/physrevb.72.113110

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A high-resolution investigation of the electron spectra close to the metal-to-insulator transition in dynamic mean-field theory is presented. An all-numerical, consistent confirmation of a smooth transition at zero temperature is provided. In particular, the separation of energy scales is verified. Unexpectedly, sharp peaks at the inner Hubbard band edges occur in the metallic regime. They are signatures of the important interaction between single-particle excitations and collective modes.
The zero-temperature core-level photoemission spectrum of a Hubbard system is studied across the metal to Mott insulator transition using dynamical mean-field theory and Wilson's numerical renormalization group [Rev. Mod. Phys. 47, 773 (1975)]. An asymmetric power-law divergence is obtained in the metallic phase with an exponent $\ensuremath{\alpha}(U,Q)\ensuremath{-}1$, which depends on the strength of both the Hubbard interaction UUU and the core-hole potential QQQ. For $Q\ensuremath{\lesssim}{U}_{c}∕2$, $\ensuremath{\alpha}$ decreases with increasing UUU and vanishes at the transition $(U\ensuremath{\rightarrow}{U}_{c})$ leading to a symmetric peak in the insulating phase. For $Q\ensuremath{\gtrsim}{U}_{c}∕2$, $\ensuremath{\alpha}$ remains finite, close to the transition, but the integrated intensity of the power law vanishes and there is no associated peak in the insulator. The weight and position of the remaining peaks in the spectra can be understood within a molecular orbital approach.
Correlated electrons in a binary alloy ${A}_{x}{B}_{1\ensuremath{-}x}$ are investigated within the Hubbard model and dynamical mean-field theory (DMFT). The random energies ${\ensuremath{\epsilon}}_{i}$ have a bimodal probability distribution and an energy separation $\ensuremath{\Delta}.$ We solve the DMFT equations by the numerical renormalization-group method at zero temperature and calculate the spectral density as a function of disorder strength $\ensuremath{\Delta}$ and interaction U at different fillings. For filling factors $\ensuremath{\nu}=x$ or 1+x1+x1+x the lower or upper alloy subband is half filled and the system becomes a Mott insulator at strong interactions, with a correlation gap at the Fermi level. At the metal-insulator transition hysteresis is observed. We also analyze the effective theory in the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Delta}}\ensuremath{\infty}$ limit and find good agreement between analytical and numerical results for the critical interaction Uc{U}_{c}Uc​ at which the metal-insulator transition occurs.
We study the Hubbard model at half band-filling on a Bethe lattice with infinite coordination number in the paramagnetic insulating phase at zero temperature. We use the dynamical mean-field theory (DMFT) mapping to a single-impurity Anderson model with a bath whose properties have to be determined self-consistently. For a controlled and systematic implementation of the self-consistency scheme we use the fixed-energy (FE) approach to the DMFT. In FE-DMFT the onset and the width of the Hubbard bands are adjusted self-consistently but the energies of the bath levels are kept fixed relatively to both band edges during the calculation of self-consistent hybridization strengths between impurity and bath sites. Using the dynamical density-matrix renormalization group method (DDMRG) we calculate the density of states with a resolution ranging from 3% of the bare bandwidth W=4tW=4tW=4t at high energies to 0.5% in the vicinity of the gap. The DDMRG resolution and accuracy for the density of states and the gap is superior to those obtained with other numerical methods in previous DMFT investigations. We find that the Mott gap closes at a critical coupling Uc/t=4.45±0.05U_{\rm c}/t=4.45 \pm 0.05Uc​/t=4.45±0.05. At U=4.5tU=4.5tU=4.5t, we observe prominent shoulders near the onset of the Hubbard bands. They are the remainders of the quasi-particle resonance in the metallic phase which appears to split when the gap opens at UcU_{\rm c}Uc​.
The zero-temperature transition from a paramagnetic metal to a paramagnetic insulator is investigated in the dynamical mean field theory for the Hubbard model. The self-energy of the effective impurity Anderson model (on which the Hubbard model is mapped) is calculated using Wilson's numerical renormalization group method. Results for the quasiparticle weight, the spectral function, and the self-energy are discussed for the Bethe and the hypercubic lattice. In both cases, the metal-insulator transition is found to occur via the vanishing of a quasiparticle resonance that appears to be isolated from the Hubbard bands.
To gain insight into the physics of the metal-insulator transition and the effectiveness of cluster dynamical mean field theory (DMFT) we have used 1, 2-, and 4-site dynamical mean field theory to solve a polaron model of electrons coupled to a classical phonon field. The metal to polaronic insulator phase boundary is determined along with electron spectral functions and cluster correlation functions. Pronounced cluster size effects occur in the intermediate coupling region in which the cluster calculation leads to a gap and the single-site approximation does not. Differences in spectra (in particular a sharper band edge in the cluster calculation) persist in the strong-coupling regime. A partial density of states is defined encoding a generalized nesting property of the band structure; variations in this density of states account for differences between the dynamical cluster approximation and the cellular-DMFT implementations of cluster DMFT, as well as for differences in behavior between the single-band models appropriate for cuprates and the multiband models appropriate for manganites. A pole or strong resonance in the self-energy is associated with insulating states; the momentum dependence of the pole is found to distinguish between Slater-like and Mott-like mechanisms for metal-insulator transition. Implications for the theoretical treatment of doped manganites are discussed.