The two-dimensional extended Hubbard model that includes a nearest-neighbor Heisenberg interaction is studied using a mean-field theory where quasiparticles are defined by an U(8) group of canonical transformations permitting both broken gauge, spin, and sublattice symmetry. The theory is further extended to incorporate a possible twist in the spin-quantization axis, so that the competition between superconductivity, charge density waves, and N\'eel and spiral antiferromagnetic order can be monitored within one single theory. Our results for positive Hubbard U and Heisenberg exchange J suggest that antiferromagnetic ordering dominates close to half-filling, while spiral states and d-wave superconductivity compete when doping is introduced. For moderate values of J, we find a phase diagram where a phase transition occurs from an antiferromagnet to a d-wave superconductor as doping is increased. A narrow region of (s+id)-wave superconductor is found for some values of J and U.
The two-dimensional extended Hubbard model that includes a nearest-neighbor Heisenberg interaction is studied using a mean-field theory where quasiparticles are defined by an U(8) group of canonical transformations permitting both broken gauge, spin, and sublattice symmetry. The theory is further extended to incorporate a possible twist in the spin-quantization axis, so that the competition between superconductivity, charge density waves, and N'eel and spiral antiferromagnetic order can be monitored within one single theory. Our results for positive Hubbard U and Heisenberg exchange J suggest that antiferromagnetic ordering dominates close to half-filling, while spiral states and d-wave superconductivity compete when doping is introduced. For moderate values of J, we find a phase diagram where a phase transition occurs from an antiferromagnet to a d-wave superconductor as doping is increased. A narrow region of (s+id)-wave superconductor is found for some values of J and U.
Abstract Using the singular-mode functional renormalization group method, we studied the doping-dependent phase diagram of the two-dimensional extended Hubbard model on square lattice. At half-filling, a variety of states strongly compete, including spin-density wave, charge-density wave, phase separation, as well as d -wave and s -wave superconductivity (SC). Upon electron doping, the system exhibits a strong preference for superconducting states. At slight dopings, the spin-density wave phase is strongly suppressed, and d -wave SC region expands into positive U , V region. At moderate dopings, a region of degenerated p -wave superconductivities emerge for positive U and negative V . Our results demonstrate how doping tunes the dominant fluctuations, suppressing density waves and stabilizing unconventional superconducting states in two dimensions.
Using functional renormalization group method, we studied the phase diagram of the one-dimensional extended Hubbard model at different dopings. At half filling, variety of states strongly compete with each other. These states include spin-density wave, charge-density wave, s-wave and p -wave superconductivity, phase separation, and an exotic bond-order wave. By doping, system favours superconductivity more than density waves. At 1/8 doping, a new area of extended s-wave superconductivity emerges between charge density wave and bond-order wave regions. If the system is doped to 1/4-doping, a new area of p -wave superconductivity emerges between charge-density wave and spin-density wave regions.
Using a path-integral formalism and decomposing the Hubbard interaction into charge and spin order parameters, we develop a 1/S loop expansion of the two-dimensional Hubbard model. At the saddle-point level, we present a detailed study of the energetics of twisted antiferromagnetic order. Doping the antiferromagnetic state leads to a rich mean-field phase diagram at zero temperature, which includes spiral phases, a column phase, and ferromagnetism. The on-site magnetization, the density of states, the plasma frequency, and the quasiparticle weights are evaluated for the twisted spin-density-wave (SDW) states as a function of doping and U/t. Doping-induced frustration remarkably leads to a closure of the Mott-Hubbard band gap for any U/t. At one-loop order, we delineate the collective spin and charge fluctuations of the mean-field SDW state. The action for the two transverse spin modes at half-filling maps to a nonlinear \ensuremath{\sigma} model, which tends to disorder upon doping. Twisted magnetic ground states exhibit a third Goldstone mode due to the complete breaking of rotational invariance. For the commensurate SDW, the charge fluctuations couple only to longitudinal spin fluctuations, whereas, for the incommensurate metallic SDW states, the charge modes are coupled nontrivially to the massless spin waves. This suggests a metallic state quite unlike traditional Fermi liquids.
We consider an extended Hubbard model of interacting fermions on a lattice. The fermion kinetic energy corresponds to a tight-binding Hamiltonian with nearest-neighbor (-t) and next-nearest-neighbor (t∣IH) hopping matrix elements. In addition to the on-site Hubbard interaction (U) we also consider a nearest-neighbor repulsion (V). We obtain the zero-temperature phase diagram of our model within the Hartree-Fock approximation. We consider ground states having charge- and spin-density-wave ordering as well as states with orbital antiferromagnetism or spin nematic order. The latter two states correspond to particle-hole binding with ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$ symmetry in the charge and spin channels, respectively. For t∣IH=0, only the charge-density-wave and spin-density-wave states are energetically stable. For nonzero t∣IH, we find that orbital antiferromagnetism (or spin nematic) order is stable over a finite portion of the phase diagram at weak coupling. This region of stability is seen to grow with increasing values of t∣IH.
The two-dimensional Hubbard model is one of the most fundamental models in condensed matter physics. It captures many properties of cuprate high-temperature superconductors. Despite its apparent simplicity, solving the Hubbard model is a challenging task. In this work, we employ the Hartree-Fock approximation, as well as functional renormalization group methods, to construct phase diagrams of the Hubbard model and to shed light on the zoo of magnetic, charge ordered, and superconducting states. The Hartree-Fock approximation can self-consistently determine the expectation values of local charge and magnetic order parameters. Mean-field theories like this can lead to a deeper understanding of the competition, coexistence and transition of different orders. We start by employing the Hartree-Fock approximation in a completely unrestricted form on finite-size lattices and complement the results with calculations in the thermodynamic limit. We construct mean-field phase diagrams of the two-dimensional Hubbard model in the thermodynamic limit for different values of the next-nearest neighbor hopping as a function of filling and temperature. We find that the dominant magnetic orders at moderate coupling strength are Néel order around half-filling, followed by spiral order, and stripe order as the hole doping is increased. We also clarify the nature of the transition from magnetic spiral to stripe order. We then extend the Hartree-Fock scheme by a functional renormalization group flow, which generates new effective interactions and allows us to also access the superconducting phase of the Hubbard model. We present an improved phase diagram, featuring Néel, spiral, and stripe order coexisting with d-wave superconductivity at low temperatures. We analyze the coexistence and competition between these orders. Finally, we perform unrestricted Hartree-Fock calculations of a Hubbard model on the graphene lattice and the Bernal bilayer graphene lattice. We also construct magnetic phase diagrams for these geometries, which feature Néel order around half-filling and various stripe orders in a secondary magnetic dome.
We examine the phase diagram of the extended Hubbard model on a square lattice, for both attractive and repulsive nearest-neighbor interactions, using CDMFT+HFD, a combination of Cluster Dynamical Mean Field theory (CDMFT) and a Hartree-Fock mean-field decoupling of the inter-cluster extended interaction. For attractive non-local interactions, this model exhibits a region of phase separation near half-filling, in the vicinity of which we find islands of d-wave superconductivity, decaying rapidly as a function of doping, with disconnected regions of extended s-wave order at smaller (higher) electron densities. On the other hand, when the extended interaction is repulsive, a Mott insulating state at half-filling is destabilized by hole doping, in the strong-coupling limit, in favor of d-wave superconductivity. At the particle-hole invariant chemical potential, we find a first-order phase transition from antiferromagnetism (AF) to d-wave superconductivity as a function of the attractive nearest-neighbor interaction, along with a deviation of the density from the half-filled limit. A repulsive extended interaction instead favors charge-density wave (CDW) order at half-filling.