Determining the properties of the two-dimensional Hubbard model is an outstanding problem in physics. Applying recent advances in constrained path auxiliary-field quantum Monte Carlo techniques and simulating large rectangular supercells, we characterize the magnetic and charge properties in the ground state as a function of doping. At intermediate interaction strengths, an incommensurate spin density wave (SDW) state is found, with antiferromagnetic order and essentially homogeneous charge correlation. The wavelength of the collective mode decreases with doping, as does its magnitude. The SDW order vanishes beyond a critical doping. As the interaction is increased, the holes go from a wavelike (delocalized) to a particlelike (localized) state, and charge ordering develops which eventually evolves into stripelike states.
Using recent advances in auxiliary-field quantum Monte Carlo techniques and the phaseless approximation to control the sign/phase problem, we determine the equation of state in the ground state of the two-dimensional repulsive single-band Hubbard model at intermediate interactions.Shell effects are eliminated and finite-size effects are greatly reduced by boundary condition integration. Spin-spin correlation functions and structure factors are also calculated. In lattice sizes up to 16 × 16, the results show signal for phase-separation. Upon doping, the system separates into one phase of density n = 1 (hole-free) and the other at density nc (∼ 0.9). The long-range antiferromagnetic order is coupled to this process, and is lost below nc.
Using exact quantum Monte Carlo calculations, we examine the interplay between localization of electronic states driven by many-body correlations and that by randomness in a two-dimensional system featuring linearly vanishing density of states at the Fermi level. A novel disorder-induced nonmagnetic insulating phase is found to emerge from the zero-temperature quantum critical point separating a semimetal and a Mott insulator. Within this phase, a phase transition from a gapless Anderson-like insulator to a gapped Mott-like insulator is identified. Implications of the phase diagram are also discussed.
The ground states of the two-dimensional repulsive Hubbard model are studied within the unrestricted Hartree-Fock (UHF) theory. Magnetic and charge properties are determined by systematic, large-scale, exact numerical calculations, and quantified as a function of electron doping h. In the solution of the self-consistent UHF equations, multiple initial configurations and simulated annealing are used to facilitate convergence to the global minimum. New approaches are employed to minimize finite-size effects in order to reach the thermodynamic limit. At low to moderate interacting strengths and low doping, the UHF ground state is a linear spin-density wave (l-SDW), with antiferromagnetic order and a modulating wave. The wavelength of the modulating wave is 2/h. Corresponding charge order exists but is substantially weaker than the spin order, hence holes are mobile. As the interaction is increased, the l-SDW states evolves into several different phases, with the holes eventually becoming localized. A simple pairing model is presented with analytic calculations for low interaction strength and small doping, to help understand the numerical results and provide a physical picture for the properties of the SDW ground state. By comparison with recent many-body calculations, it is shown that, for intermediate interactions, the UHF solution provides a good description of the magnetic correlations in the true ground state of the Hubbard model.
We investigate ground state properties of the half-filled staggered-flux Hubbard model on a square lattice. Energy gaps to charge and spin excitations and magnetic as well as dimer orders are calculated as a function of interaction strength U/t by means of constrained-path quantum Monte Carlo method. It is found that the system is a semi-metal at U/t 5.6 and a Mott insulator with long-range antiferromagnetic order at U/t 6.6. In the range 5.6 U/t 6.6, the ground state is an correlated insulator where both magnetic and dimer orders are absent. Furthermore, spin excitation in the intermediate phase appears to be gapless, and the measured spin-spin correlation function exhibits power-law decaying behavior. The data suggest that the non-magnetic ground state is a possible candidate for the putative algebraic spin liquid. Model Hamiltonians have played an important role in realizing such exotic spin liquid states [4, 5]. Evidence of spin liquid phases has been found in the spin 1/2 Heisenberg model on triangular lattices[6], square lattices with frustration [7][8][9], and kagome lattices [10]. In these geometrically frustrated systems[11], antiferromagnetic (AF) orders are suppressed by strong quantum fluctuations. In addition to spin systems, there is also progress using the Hubbard model which contains spin and charge degrees of freedom. Spin liquid ground states have been identified in the model on anisotropic triangular lattices [12] and on bipartite honeycomb lattices [13].In this paper, we examine ground state properties of the half-filled staggered-flux Hubbard model (sfHM) on a square lattice. As will be seen later, low energy physics in the sfHM is described by Dirac fermions, similar to that found in the Hubbard model on honeycomb lattices [13]. The model is defined by the Hamiltonianwhere t ij = t e iθ ij is the nearest-neighbor hopping and we set t = 1 throughout this work. The operator c iσ (c iσ ) creates (annihilates) an electron with spin σ =↑, ↓ at site i on a lattice of size N = L × L. U > 0 is the onsite Coulomb repulsion. We work in the canonical ensemble.An electron gains a phase Φ = θ ij when it hops around a plaquette of the square lattice. Φ = 0 corresponds to the original Hubbard model. We focus on the case Φ = π in the present study. There is a gauge freedom in choosing θ ij . Here we distribute the phase
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