We investigate the effect of assisted hopping in the Anderson impurity model. We use the flow equation method, which, by means of unitary transformations, generates a sequence of Hamiltonians in order to eliminate the assisted hopping terms. This approach yields a renormalized on-site energy ${\ensuremath{\epsilon}}_{d}^{*},$ a renormalized correlation energy
U∗, and other terms, which include pair hopping. For some parameter values, the initial Hamiltonian flows towards an attractive Anderson model. We argue that this result implies a tendency towards local pairing fluctuations.
We investigate static and dynamical ground-state properties of the two-impurity Anderson model at half filling in the limit of vanishing impurity separation using the dynamical density-matrix renormalization group method. In the weak-coupling regime, we find a quantum phase transition as a function of inter-impurity hopping driven by the charge degrees of freedom. For large values of the local Coulomb repulsion, the transition is driven instead by a competition between local and non-local magnetic correlations. We find evidence that, in contrast to the usual phenomenological picture, it seems to be the bare effective exchange interactions which trigger the observed transition.
The effect of interchain hopping and interaction on Anderson localization has been investigated for two coupled chains of spinless fermions with nearest neighbor interaction. Using the renormalization group method, we find that interchain hopping plays a significant role when the correlation gap induced by the interplay of interchain hopping and intrachain interaction becomes larger than the Anderson localization energy scale induced by impurities. The strong competition between localization and delocalization is examined for attractive interaction.
The effect of interchain hopping and interaction on Anderson localization has been investigated for two coupled chains of spinless fermions with nearest neighbor interaction. Using the renormalization group method, we find that interchain hopping plays a significant role when the correlation gap induced by the interplay of interchain hopping and intrachain interaction becomes larger than the Anderson localization energy scale induced by impurities. The strong competition between localization and delocalization is examined for attractive interaction.
Our previous mean-field study concerning superconducting pairings in the extended Hubbard model with on-site repulsive and intersite attractive interaction and arbitrary electron density is extended to include the effects of nearest-neighbor exchange (
J) and correlated hopping (
K) interaction. Detailed numerical analysis of
s-,
p-, and
d-wave pairing solutions is performed for the two-dimensional square lattice with nearest- (
t) and next-nearest- (
t2) neighbor hopping, and the resulting mutual stability phase diagrams are given as a function of band filling and the interaction parameters. Antiferromagnetic exchange can enhance both the
d-wave and the extended
s-wave pairing. If it prevails over the repulsive intersite density-density interaction, such a term can be a leading mechanism for superconductivity. However, its effects strongly depend on the band filling and the
tt2 ratio, giving in particular for
t2=0 s-wave (
d-wave) pairing as most favorable in the low (high) density limit, but increasing
t2 can even reverse this tendency. The correlated hopping term which breaks the electron-hole symmetry affects
s-wave pairing mostly. A condensation transition (phase separation), possible in the presence of the attractive density-density interaction, is also analyzed within the random-phase approximation, and stability conditions of such an electron droplet phase with respect to other types of ordering are determined as a function of the band filling for the two-dimensional square lattice.
We study the ground-state phase diagram of the Anderson-Hubbard model with correlated hopping at half-filling in one dimension. The Hamiltonian has a local Coulomb repulsion
U and a disorder potential with local energies randomly distributed in the interval $(\ensuremath{-}W,+W)$ with equal probability, acting on the singly occupied sites. The hopping process which modifies the number of doubly occupied sites is forbidden. The hopping between nearest-neighbor singly occupied and empty sites or between singly occupied and doubly occupied sites has the same amplitude
t. We identify three different phases as functions of the disorder amplitude
W and Coulomb interaction strength
U>0. When
U<4t the system shows a metallic phase: (i) only when no disorder is present
W=0 or an Anderson-localized phase, (ii) when disorder is introduced $W\ensuremath{\ne}0$. When
U>4t the Anderson-localized phase survives as long as disorder effects dominate on the interaction effects, otherwise a Mott-insulator phase (iii) arises. Phases (i) and (ii) are characterized by a finite density of doublons and a vanishing charge gap among the ground state and the excited states. Phase (iii) is characterized by the vanishing density of doublons and a finite gap for the charge excitations.