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Groundstate magnetism of the one-band Hubbard model on the frustrated square lattice where both nearest-neighbour $t_1$ and next-nearest-neighbour $t_2$ hoppings are considered at half-filling are revisited within mean field approximation. Two new magnetic phases are detected at intermediate strength of Hubbard $U$ and relative strong frustration of $t_2/t_1$, named double-stripe and plaquette antiferromagnetic states, both of which are metallic and stable even at finite temperature and electron doping. The nature of the phase transitions between different phases and the properties of the two new states are analyzed in detail. Our results of various magnetic states emerging from geometric frustration in the minimal model suggests that distinct antiferromagnetism observed experimentally in the parent states of two high-T$_c$ superconducting families, i.e., cuprates and iron-based superconductors, may be understood from a unified microscopic origin, irrespective of orbital degrees of freedom, or hoppings further than next-nearest neighbour, etc.
We explore a variational Ansatz for lattice quantum systems -- named long-range entangled-plaquette state -- in which pairs of clusters of adjacent lattice sites are correlated at any distance. The explicit scale-free structure of correlations built
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 employ a variational Monte Carlo approach to efficiently obtain the dynamical structure factor for the spin-1/2 $J_1-J_2$ Heisenberg model on the square lattice. Upon increasing the frustrating ratio $J_2/J_1$, the ground state undergoes a continu
We employ the Hartree-Fock approximation to identify the magnetic ground state of the Hubbard model on a frustrated square lattice. We investigate the phase diagram as a function of the Coulomb repulsions strength $U$, and the ratio $t/t$ between the
We study the field dependence of the antiferromagnetic spin-1/2 Heisenberg model on the square lattice by means of exact diagonalizations. In a first part, we calculate the spin-wave velocity, the spin-stiffness, and the magnetic susceptibility and t