The authors use an unrestricted self-consistent mean-field approach to the one-dimensional periodic Hubbard model to study its ground-state phase diagram. Their approach allows one to incorporate spin and electron correlations as well as spin and charge fluctuations. The authors find that a homogeneous antiferromagnetic state exists only at half-filling, where the state is also insulating. Off half-filling, it was found that the ground state of the Hubbard model consists of clusters with different magnetic and charge properties. For certain values of the parameters of the system the cluster formation develops to a full phase separation. The effects of the intersite repulsive or attractive interaction on the ground-state properties were also examined. Implications of the authors results for the existence of a superconducting ground state as well as comparison with other studies will be briefly discussed.
The authors use an unrestricted self-consistent mean-field approach to the one-dimensional periodic Hubbard model to study its ground-state phase diagram. Their approach allows one to incorporate spin and electron correlations as well as spin and charge fluctuations. The authors find that a homogeneous antiferromagnetic state exists only at half-filling, where the state is also insulating. Off half-filling, it was found that the ground state of the Hubbard model consists of clusters with different magnetic and charge properties. For certain values of the parameters of the system the cluster formation develops to a full phase separation. The effects of the intersite repulsive or attractive interaction on the ground-state properties were also examined. Implications of the authors results for the existence of a superconducting ground state as well as comparison with other studies will be briefly discussed.
We use the correlated-random-field approximation and a conditional coherent-potential approximation to study the ground-state phase diagram of the one-band Hubbard model. Our approach incorporates both spin and electron correlations. It has been found that for certain values of the parameters of the model, in addition to paramagnetic, ferromagnetic, antiferromagnetic, and spin-glass or spin-liquid phases found in our earlier studies, a phase-separated phase is found to be favored for 0.7\ensuremath{\le}n\ensuremath{\le}1.0 and U/B\ensuremath{\ge}2 in good agreement with results obtained in the t-J model using the technique of the 1/N expansion. The present approach also allows one to watch the dependence of the electron density of states on the number of electrons per site and gives a single physical picture for the occurrence of a metal-insulator transition. Implications of these results for the existence of superconducting ground state as well as comparison to other studies will be briefly discussed.
Cooperation and competition between the antiferromagnetic, d-wave superconducting, and Mott-insulating states are explored for the two-dimensional Hubbard model including nearest and next-nearest-neighbor hoppings at zero temperature. Using the variational cluster approach with clusters of different shapes and sizes up to 10 sites, it is found that the doping-driven transition from a phase with microscopic coexistence of antiferromagnetism and superconductivity to a purely superconducting phase is discontinuous for strong interaction and accompanied by phase separation. At half-filling the system is in an antiferromagnetic Mott-insulating state with vanishing charge compressibility. Upon decreasing the interaction strength U below a certain critical value of roughly ${U}_{c}\ensuremath{\sim}4$ (in units of the nearest-neighbor hopping), however, the filling-dependent magnetic transition changes its character and becomes continuous. Phase separation or, more carefully, the tendency towards the formation of inhomogeneous states disappears. This critical value is in contrast to previous studies, where a much larger value was obtained. Moreover, we find that the system at half-filling undergoes the Mott transition from an insulator to a state with a finite charge compressibility at essentially the same value. The weakly correlated state at half-filling exhibits superconductivity microscopically admixed to the antiferromagnetic order. This scenario suggests a close relation between phase separation and the Mott-insulator physics.
The exact phase diagrams of the one-dimensional Hubbard model, both attractive and repulsive, in the presence of an arbitrary magnetic field h for various electron concentrations n and on-site interaction strengths U <0 or U >0 are calculated and investigated. The exact ground-state properties, namely, the ground-state energy, the average spin (magnetization), the concentration of the doubly occupied sites, the kinetic energy, the chemical potential, the spin (magnetic) susceptibility and the charge compressibility, are calculated and examined over a wide range of interaction strengths U for various h and n . It is found that the spin susceptibility at half-filling is non-analytic and changes discontinuously as U →0. The exact theory shows the absence of a charge energy gap in the U ⩽0 region for all n and provides, for the chemical potential, the rigorous upper and lower bounds for half-filled and empty bands respectively. The analytical results derived for the weak-coupling limit and asymptotic expansions for strong coupling are in full agreement with the numerical calculations.
We study the phase diagram of the one-dimensional U-V model at quarter filling in the most general case where the on-site and first-neighbor interactions U and V can be both attractive and repulsive. The results have been obtained using exact diagonalization of small clusters and variational techniques, as well as exact results in various limits. We have analyzed four properties of the ground state: (i) whether it is insulating or metallic; (ii) whether it is homogeneous or phase separated; (iii) whether it has a spin gap; (iv) whether it has dominant superconducting fluctuations. With eight phases, the resulting phase diagram is unexpectedly rich. The four phases not found in the weak coupling limit are: (i) an insulating phase when U and V are large enough; (ii) a region of phase separation when V is attractive; (iii) another region of phase separation when V is large enough and U small; (iv) a region with dominant superconducting fluctuations when V is intermediate and U small. The actual nature of this last plase, which has pairs but no spin gap, is not fully clear yet.
Using the Hubbard chain at quarter filling as a model system, we study the ground state properties of highly doped antiferromagnets. In particular, the Hubbard chain at quarter filling is unstable against 2kF- and 4kF-periodic potentials, leading to a large variety of charge and spin ordered ground states. Employing the density matrix renormalization group method, we compare the energy gain of the ground state induced by different periodic potentials. For interacting systems the lowest energy is found for a 2kF-periodic magnetic field, resulting in a band insulator with spin gap. For strong interaction, the 4kF-periodic potential leads to a half-filled Heisenberg chain and thus to a Mott insulating state without spin gap. This ground state is more stable than the band insulating state caused by any non-magnetic 2kF-periodic potential. Adding more electrons, a cluster-like ordering is preferred.
We determine the spin and charge orders in the ground state of the doped two-dimensional (2D) Hubbard model in its simplest form, namely with only nearest-neighbor hopping and on-site repulsion. At half-filling, the ground state is known to be an antiferromagnetic Mott insulator. Doping Mott insulators is believed to be relevant to the superconductivity observed in cuprates. A variety of candidates have been proposed for the ground state of the doped 2D Hubbard model. A recent work employing a combination of several state-of-the-art numerical many-body methods established the stripe order as the ground state near 1/8 doping at strong interactions. In this paper, we apply one of these methods, the cutting-edge constrained-path auxiliary field quantum Monte Carlo (AFQMC) method with self-consistently optimized gauge constraints, to systematically study the model as a function of doping and interaction strength. With careful finite size scaling based on large-scale computations, we map out the ground state phase diagram in terms of its spin and charge order. We find that modulated antiferromagnetic order persists from near half-filling to about 1/5 doping. At lower interaction strengths or larger doping, these ordered states are best described as spin-density waves, with essentially delocalized holes and modest oscillations in charge correlations. When the charge correlations are stronger (large interaction or small doping), they are best described as stripe states, with the holes more localized near the node in the antiferromagnetic spin order. In both cases, we find that the wavelength in the charge correlations is consistent with so-called filled stripes.