We address some open questions regarding the phase diagram of the one-dimensional Hubbard model with asymmetric hopping coefficients and balanced species. In the attractive regime we present a numerical study of the passage from on-site pairing dominant correlations at small asymmetries to charge-density waves in the region with markedly different hopping coefficients. In the repulsive regime we exploit two analytical treatments in the strong- and weak-coupling regimes in order to locate the onset of phase separation at small and large asymmetries respectively.
The recent discovery of superconductivity under high pressure in the ladder compound BaFe$_2$S$_3$ has opened a new field of research in iron-based superconductors with focus on quasi one-dimensional geometries. In this publication, using the Density Matrix Renormalization Group technique, we study a two-orbital Hubbard model defined in one dimensional chains. Our main result is the presence of hole binding tendencies at intermediate Hubbard $U$ repulsion and robust Hund coupling $J_H/U=0.25$. Binding does not occur neither in weak coupling nor at very strong coupling. The pair-pair correlations that are dominant near half-filling, or of similar strength as the charge and spin correlation channels, involve hole-pair operators that are spin singlets, use nearest-neighbor sites, and employ different orbitals for each hole. The Hund coupling strength, presence of robust magnetic moments, and antiferromagnetic correlations among them are important for the binding tendencies found here.
We show that optical excitation of the Mott insulating phase of the one-dimensional Hubbard model can create a state possessing two of the hallmarks of superconductivity: a nonvanishing charge stiffness and long-ranged pairing correlation. By employing the exact diagonalization method, we find that the superposition of the $eta$-pairing eigenstates induced by the optical pump exhibits a nonvanishing charge stiffness and a pairing correlation that decays very slowly with system size in sharp contrast to the behavior of an ensemble of thermally excited eigenstates, which has a vanishing charge stiffness and no long-ranged pairing correlations. We show that the charge stiffness is indeed directly associated with the $eta$-pairing correlation in the Hubbard model. Our finding demonstrates that optical pumping can actually lead to superconducting-like properties on the basis of the $eta$-pairing states.
The paramagnetic phase diagram of the Hubbard model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping on the Bethe lattice is computed at half-filling and in the weakly doped regime using the self-energy functional approach for dynamical mean-field theory. NNN hopping breaks the particle-hole symmetry and leads to a strong asymmetry of the electron-doped and hole-doped regimes. Phase separation occurs at and near half-filling, and the critical temperature of the Mott transition is strongly suppressed.
By using variational wave functions and quantum Monte Carlo techniques, we investigate the interplay between electron-electron and electron-phonon interactions in the two-dimensional Hubbard-Holstein model. Here, the ground-state phase diagram is triggered by several energy scales, i.e., the electron hopping $t$, the on-site electron-electron interaction $U$, the phonon energy $omega_0$, and the electron-phonon coupling $g$. At half filling, the ground state is an antiferromagnetic insulator for $U gtrsim 2g^2/omega_0$, while it is a charge-density-wave (or bi-polaronic) insulator for $U lesssim 2g^2/omega_0$. In addition to these phases, we find a superconducting phase that intrudes between them. For $omega_0/t=1$, superconductivity emerges when both $U/t$ and $2g^2/tomega_0$ are small; then, by increasing the value of the phonon energy $omega_0$, it extends along the transition line between antiferromagnetic and charge-density-wave insulators. Away from half filling, phase separation occurs when doping the charge-density-wave insulator, while a uniform (superconducting) ground state is found when doping the superconducting phase. In the analysis of finite-size effects, it is extremely important to average over twisted boundary conditions, especially in the weak-coupling limit and in the doped case.
By employing unbiased numerical methods, we show that pulse irradiation can induce unconventional superconductivity even in the Mott insulator of the Hubbard model. The superconductivity found here in the photoexcited state is due to the $eta$-pairing mechanism, characterized by staggered pair-density-wave oscillations in the off-diagonal long-range correlation, and is absent in the ground-state phase diagram; i.e., it is induced neither by a change of the effective interaction of the Hubbard model nor by simple photocarrier doping. Because of the selection rule, we show that the nonlinear optical response is essential to increase the number of $eta$ pairs and thus enhance the superconducting correlation in the photoexcited state. Our finding demonstrates that nonequilibrium many-body dynamics is an alternative pathway to access a new exotic quantum state that is absent in the ground-state phase diagram and also provides an alternative mechanism for enhancing superconductivity.
L. Barbiero
,M. Casadei
,M. Dalmonte
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(2010)
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"Phase separation and pairing regimes in the one-dimensional asymmetric Hubbard model"
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Cristian Degli Esposti Boschi
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