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Physical Review B

Dynamics of two interacting electrons in Anderson-Hubbard chains with long-range correlated disorder: Effect of a static electric field

Wandearley S. Dias, Elton Malta Nascimento, M. L. Lyra, F. A. B. F. de Moura

Published Jan 13, 2010• 18 citations
Publisher

Abstract

We investigate the influence of the on-site Hubbard interaction $U$ on the eigenstates and dynamics of two electrons restricted to move in a linear chain with long-range correlated disorder. We solve the time-dependent Schr\"odinger equation to follow the time evolution of an initially localized Gaussian two-electron wave packet. In the regime of strongly correlated disorder, for which one-electron extended eigenstates emerge near the band center, the electron-electron coupling promotes the trapping of a finite portion of the wave packet. In the presence of a uniform electric field, the wave packet develops complex Bloch oscillations. The power spectrum of the centroid's velocity trace shows a splitting near the typical semiclassical Bloch frequency, as well as a frequency doubling phenomenon for intermediate couplings which is related to the bounded states components that are present in the wave packet. Finally, we show that localized and extended two-electron eigenstates coexist near the band center with the level spacing distribution showing a universal Poissonian form irrespective to the Hubbard coupling.

DOI
10.1103/physrevb.81.045116

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We investigate the influence of the on-site Hubbard interaction UUU on the eigenstates and dynamics of two electrons restricted to move in a linear chain with long-range correlated disorder. We solve the time-dependent Schr"odinger equation to follow the time evolution of an initially localized Gaussian two-electron wave packet. In the regime of strongly correlated disorder, for which one-electron extended eigenstates emerge near the band center, the electron-electron coupling promotes the trapping of a finite portion of the wave packet. In the presence of a uniform electric field, the wave packet develops complex Bloch oscillations. The power spectrum of the centroid's velocity trace shows a splitting near the typical semiclassical Bloch frequency, as well as a frequency doubling phenomenon for intermediate couplings which is related to the bounded states components that are present in the wave packet. Finally, we show that localized and extended two-electron eigenstates coexist near the band center with the level spacing distribution showing a universal Poissonian form irrespective to the Hubbard coupling.
We study numerically the effect of the on-site Hubbard interaction UUU on the dynamics of two electrons subjected to an external electric field and restricted to move in a linear chain with open boundaries. We solve the time-dependent Schr\"odinger equation to follow the time evolution of an initially localized two-electron state. For electrons initially far apart, the wave packet develops Bloch oscillations whose characteristic frequency is in agreement with a semiclassical calculation. For initially close electrons in a singlet state, a frequency doubling sets up, which is more pronounced for intermediate couplings. We discuss this effect by revealing the opposite trends the electron-electron coupling produces on the wave-packet components corresponding to bounded and unbounded states.
We investigate the spectral properties and the dynamics of doublons in the one-dimensional Hubbard model at infinite temperature. Using a Chebyshev expansion approach formulated in the superfermionic representation, we compute the momentum- and frequency-resolved doublon spectral function across a wide range of interaction strengths UUU and in the presence of an external electric field. Increasing the interaction, the spectrum gradually splits into separate bands associated with two-hole and two-particle excitations. Despite the presence of strong correlations, we find that doublons retain their coherence and undergo long-lived Bloch oscillations, as well as rich quantum walk dynamics characterized by light-cone spreadings at strong coupling, which we analyze through the time-and space-resolved Green's function.
Using the time-dependent density-matrix renormalization group, we study the time evolution of electronic wave packets in the one-dimensional extended Hubbard model with on-site and nearest-neighbor repulsion, UUU and VVV, respectively. As expected, the wave packets separate into spin-only and charge-only excitations (spin-charge separation). Charge and spin velocities exhibit nonmonotonic dependence on VVV. For small and intermediate values of VVV, both velocities increase with VVV. However, the charge velocity exhibits a stronger dependence than that of the spin, leading to a more pronounced spin-charge separation. Charge fractionalization, on the other hand, is weakly affected by VVV. The results are explained in terms of Luttinger liquid theory in the weak-coupling limit and an effective model in the strong-coupling regime.
It is well known that an electron in a single-band tight-binding lattice coherently driven by an external dc electric field undergoes Bloch oscillations. In the framework of the extended Hubbard model, here it is shown theoretically that two strongly interacting electrons with on-site and nearest-neighbor site repulsion undergo a sequence of Bloch oscillations and Zener tunneling, the so-called Bloch-Zener oscillations (BZOs), among different narrow bands formed by bound particle states. Such a kind of BZOs arise because of nearest-neighbor site particle interaction and are thus rather distinct than BZOs observed for a single electron in biperiodic lattices supporting two single-particle minibands.
We study the quantum dynamics of a strongly correlated electron pair in a one-dimensional lattice, focusing on the occurrence of local dissociation/pairing mechanisms induced by a site energy defect. To this end, we simulate the time evolution of two interacting electrons on a finite-size chain governed by an extended Hubbard Hamiltonian including on-site Coulomb repulsion UUU and nearest-neighbor interaction VVV, along with single-electron hopping JJJ. By introducing a local site energy defect with amplitude $\mathrm{\ensuremath{\Delta}}$, we show that a transition between spatially paired/dissociated electrons can occur in the vicinity of this site. Such mechanisms arise in a strongly correlated regime with nonzero nearest-neighbor Coulomb interactions and under the conditions $(U\ensuremath{\sim}V\ensuremath{\sim}\mathrm{\ensuremath{\Delta}})\ensuremath{\gg}J$. To rationalize these phenomena, we reformulate the two-electron dynamics of the original Hubbard chain as an effective single-particle problem on a two-dimensional network. Within this framework, we show that the pairing/dissociation dynamics are driven by resonances between two distinct families of two-electron eigenstates: (i) states with two spatially well-separated electrons with one located at the site defect, and (ii) states with a locally bound electron located away from the defect. At resonance, these states hybridize, allowing transitions from locally paired to dissociated electrons---and vice versa---in the vicinity of the defect. These results provide further insights into exotic pairing phenomena in strongly correlated electronic systems and may have implications for the design of tunable many-body states in low-dimensional quantum materials.
Interplay of electron correlation and randomness is studied by using the Anderson-Hubbard model within the Hartree-Fock approximation. Under the coexistence of short-range interaction and diagonal disorder, we obtain the ground-state phase diagram in three dimensions, which includes an antiferromagnetic insulator, an antiferromagnetic metal, a paramagnetic insulator (Anderson-localized insulator) and a paramagnetic metal. Although only the short-range interaction is present in this model, we find unconventional soft gaps in the insulating phases irrespective of electron filling, spatial dimensions and long-range order, where the single-particle density of states (DOS) vanishes with a power-law scaling in one dimension (1D) or even faster in two dimensions (2D) and three dimensions (3D) toward the Fermi energy. We call it soft Hubbard gap. Moreover, exact-diagonalization results in 1D support the formation of the soft Hubbard gap beyond the mean-field level. The formation of the soft Hubbard gap cannot be attributed to a conventional theory by Efros and Shklovskii (ES) owing the emergence of soft gaps to the long-range Coulomb interaction. Indeed, based on a picture of multivalley energy landscape, we propose a phenomenological scaling theory, which predicts a scaling of the DOS in perfect agreement with the numerical results. We further discuss a correction of the scaling of the DOS by the long-range part of the Coulomb interaction, which modifies the scaling of Efros and Shklovskii. Furthermore, explicit formulae for the temperature dependence of the DC resistivity via variable-range hopping under the influence of the soft gaps are derived. Finally, we compare the present theory with experimental results of SrRu_{1-x}Ti_xO_3.