Abstract
The number of electronic bands is usually considered invariant regardless of the electron density in a band picture. However, in interacting systems, the spectral-weight distribution generally changes depending on the electron density, and electronic states can even emerge or disappear as the electron density changes. Here, to clarify how electronic states emerge and become dominant as the electron density changes, the spectral function of the Hubbard ladder with strong repulsion and strong intrarung hopping is studied using the non-Abelian dynamical density-matrix renormalization-group method. A mode emerging in the low-electron-density limit gains spectral weight as the electron density increases and governs the dimer Mott physics at quarter-filling. In contrast, the antibonding band, which is dominant in the low-electron-density regime, loses spectral weight and disappears at the Mott transition at half-filling, exhibiting the momentum-shifted magnetic dispersion relation in the small-doping limit. This paper identifies the origin of the electronic states responsible for the Mott transition and brings a new perspective to electronic bands by revealing the overall nature of electronic states over a wide energy and electron-density regime.
Highlights
In band theory, an electron is assumed to hop from one atomic orbital to another in an effective periodic potential, forming a band [1]; the number of bands is considered essentially determined by the number of atomic orbitals in a unit cell, which does not change with the electron density
To clarify the evolution of electronic states as a function of the electron density, we investigate the spectral function in the overall electrondensity regime primarily for U t⊥ t > 0 (Ut /t⊥2 is not too large for the ground state to have spin 0 or 1/2 [19,20]) based on the numerical results for U/t = 16 and t⊥/t = 2 obtained using the non-Abelian dynamical densitymatrix renormalization-group (DDMRG) method [5,22,23,24,25,26,27]
In the small-doping limit, the dispersion relation reduces to the magnetic dispersion relation shifted by the Fermi momentum kF = (π, 0) (Fig. 6)
Summary
An electron is assumed to hop from one atomic orbital to another in an effective periodic potential, forming a band [1]; the number of bands is considered essentially determined by the number of atomic orbitals in a unit cell, which does not change with the electron density. The essence of electronic correlations, is investigated in the regime of strong Coulomb repulsion and strong intrarung hopping. The main features we focus on in this paper are the (1) emergent electronic states in the low-electron-density regime [Sec. V], (2) spectral-weight transfer from the dominant modes to the emergent modes, which makes the emergent modes dominant, whereas the dominant modes significantly lose spectral weight as the electron density increases to halffilling [Sec. III], (3) dimer Mott gap at quarter-filling, whose value is significantly limited by the intrarung hopping in the strong-Coulomb-repulsion regime [Sec. VI], and (4) emergent electronic states upon doping a Mott insulator by which the Mott transition is characterized [Sec. VIII]. The above features are contrasted with conventional views, such as a band picture
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