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Register a new userCharge stiffness and long-range correlation in the optically induced $eta$-pairing state of the one-dimensional Hubbard model
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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.
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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 show how, upon heating the spin degrees of freedom of the Hubbard model to infinite temperature, the symmetries of the system allow the creation of steady-states with long-range correlations between $eta$-pairs. With induce this heating with either dissipation or periodic driving and evolve the system towards a nonequilibrium steady state, a process which melts all spin order in the system. The steady state is identical in both cases and displays distance-invariant off-diagonal $eta$-correlations. These correlations were first recognised in the superconducting eigenstates in Yangs seminal paper [Phys. Rev. Lett 63, 2144 (1989)], which are a subset of our steady states. We show that our results are a consequence of symmetry properties and entirely independent of the microscopic details of the model and the heating mechanism.
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.
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.
We study the real-time and real-space dynamics of charge in the one-dimensional Hubbard model in the limit of high temperatures. To this end, we prepare pure initial states with sharply peaked density profiles and calculate the time evolution of these nonequilibrium states, by using numerical forward-propagation approaches to chains as long as 20 sites. For a class of typical states, we find excellent agreement with linear-response theory and unveil the existence of remarkably clean charge diffusion in the regime of strong particle-particle interactions. Moreover, we demonstrate that this diffusive behavior does not depend on certain details of our initial conditions, i.e., it occurs for five different realizations with random and nonrandom internal degrees of freedom, single and double occupation of the central site, and displacement of spin-up and spin-down particles.
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