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Register a new userFlat band and $eta $-pairing states in one-dimensional Moir{e} Hubbard model
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A moir{e} system is formed when two periodic structures have a slightly mismatched period, resulting in unusual strongly correlated states in the presence of particle-particle interactions. The periodic structures can arise from the intrinsic crystalline order and periodic external field. We investigate a one-dimensional Hubbard models with periodic on-site potential of period $n_{0}$, which is commensurate to the lattice constant. For large $% n_{0}$, exact solution demonstrates that there is a midgap flat band with zero energy in the absence of Hubbard interaction. Each moir{e} unit cell contributes two zero energy levels to the flat band. In the presence of Hubbard interaction, the midgap physics is demonstrated to be well described by a uniform Hubbard chain, in which the effective hopping and on-site interaction strength, can be controlled by the amplitude and period of the external field. Numerical simulations are performed to demonstrate the correlated behaviors in the finite-sized moir{e} Hubbard system, including the existence of $eta $-pairing state, and bound pair oscillation. This finding provides a method to enhance the correlated effect by a spatially periodic external field.
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The introduction of non-Hermiticity has greatly enriched the research field of traditional condensed matter physics, and eventually led to a series of discoveries of exotic phenomena. We investigate the effect of non-Hermitian imaginary hoppings on the attractive Hubbard model. The exact bound-pair solution shows that the electron-electron correlation suppresses the non-Hermiticity, resulting in off-diagonal long-range order (ODLRO) ground state. In a large negative $U $ limit, the ODLRO ground state corresponds to $eta $-spin ferromagnetic states. We also study the system with mixed hopping configuration. The numerical result indicates the existence of the transition from normal to $eta $-pairing ground states by increasing the imaginary hopping strength. Our results provide a promising approach for the non-Hermitian strongly correlated system.
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.
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.
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.
Employing the density-matrix renormalization group technique in the matrix-product-state representation, we investigate the photoexcited superconducting correlations induced by the $eta$-pairing mechanism in the half-filled Hubbard chain. We estimate the characteristic pair correlation function and verify the accuracy of our numerical results by comparison with exact-diagonalization data for small systems. The optimal parameter set of the pump that most enhances the $eta$-pair correlations, is calculated in the strong-coupling regime. For such a pump, we explore the possibility of quasi-long-range order.
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