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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 $eta$-pairin
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 crystal
We study the Hubbard model with non-Hermitian asymmetric hopping terms. The conjugate hopping terms are introduced for two spin components so that the negative sign is canceled out. This ensures that the quantum Monte Carlo simulation is free from th
The previous theoretical study has shown that pulse irradiation to the Mott insulating state in the Hubbard model can induce the enhancement of superconducting correlation due to the generation of $eta$ pairs. Here, we show that the same mechanism ca
The two-dimensional attractive Hubbard model is studied in the weak to intermediate coupling regime by employing a non-perturbative approach. It is first shown that this approach is in quantitative agreement with Monte Carlo calculations for both sin