Quantum Monte Carlo study of the two-dimensional fermion Hubbard model (original) (raw)
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Correlation effects on the Fermi surface of the two-dimensional Hubbard model
Journal of Physics and Chemistry of Solids, 2002
Effects of electron correlation on the Fermi surface is investigated for the twodimensional Hubbard model by the quantum Monte Carlo method. At first, an infinitesimal doping from the half filling is focused on and the momentum dependent charge susceptibility κ(k) = dn(k) dµ is calculated at a finite temperature. At the temperature T ∼ t 2 U , it shows peak structure at (±π/2, ±π/2) on the Fermi surface (line). It is consistent with the mean-field prediction of the d-wave pairing state or the staggerd flux state. This momentum dependent structure disappears at the high temperature T ≈ U. After summarizing the results of the half filling case, we also discuss the effects of the doping on the momentum dependent charge susceptibility. The anisotropic structure at half filling fades out with sufficient doping.
Physical Review B
Using first-principle Hybrid-Monte-Carlo (HMC) simulations, we carry out an unbiased study of the competition between spin-density wave (SDW) and charge-density wave (CDW) order in the extended Hubbard model on the two dimensional hexagonal lattice at half filling. We determine the phase diagram in the space of on-site and nearest-neighbor couplings U and V in the region V < U/3, which can be simulated without a fermion sign problem, and find that a transition from semimetal to a SDW phase occurs at sufficiently large U for basically all V. Tracing the corresponding phase boundary from V = 0 to the V = U/3 line, we find evidence for critical scaling in the Gross-Neveu universality class for the entire boundary. With rather high confidence we rule out the existence of the CDW ordered phase anywhere in the range of parameters considered. We also discuss several improvements of the HMC algorithm which are crucial to reach these conclusions, in particular the improved fermion action with exact sublattice symmetry and the complexification of the Hubbard-Stratonovich field to ensure the ergodicity of the algorithm.
Physical Review B, 2001
We study the effects of disorder on long-range antiferromagnetic correlations in the half-filled, two dimensional, repulsive Hubbard model at T = 0. A mean field approach is first employed to gain a qualitative picture of the physics and to guide our choice for a trial wave function in a constrained path quantum Monte Carlo (CPQMC) method that allows for a more accurate treatment of correlations. Within the mean field calculation, we observe both Anderson and Mott insulating antiferromagnetic phases. There are transitions to a paramagnet only for relatively weak coupling, U < 2t in the case of bond disorder, and U < 4t in the case of on-site disorder. Using ground state CPQMC we demonstrate that this mean field approach significantly overestimates magnetic order. For U = 4t, we find a critical bond disorder of Vc ≈ (1.6 ± 0.4)t even though within mean field theory no paramagnetic phase is found for this value of the interaction. In the site disordered case, we find a critical disorder of Vc ≈ (5.0 ± 0.5)t at U = 4t.
Quantum Monte Carlo simulation of the triangular lattice in the repulsive Hubbard model
Surface Science, 2001
The repulsive Hubbard model for the triangular lattice in two dimensions is studied by means of a quantum Monte Carlo simulation in the grand canonical ensemble. Both on-site and nearest neighbor Coulomb interactions are taken into account. The one-electron spectral function Akx is shown to gradually develop a gap as the temperature is lowered provided the Hubbard U is larger than the bandwidth. Analysis of the spin and charge structure factors (static correlation functions) shows that, while the charge factor remains featureless, the spin factor develops a strong peak very close to the M H point 2p=3; 0 of the small surface Brillouin zone (corresponding to the three-sublattice model). Implications for the behavior of the 3 p  3 p adlayer structures on fourth-group semiconductor surfaces are brie¯y commented upon. Ó
Effect of interactions, disorder and magnetic field in the Hubbard model in two dimensions
Pramana, 2005
The effects of both interactions and Zeeman magnetic field in disordered electronic systems are explored in the Hubbard model on a square lattice. We investigate the thermodynamic (density, magnetization, density of states) and transport (conductivity) properties using determinantal quantum Monte Carlo and inhomogeneous Hartree Fock techniques. We find that at half filling there is a novel metallic phase at intermediate disorder that is sandwiched between a Mott insulator and an Anderson insulator. The metallic phase is highly inhomogeneous and coexists with antiferromagnetic long-range order. At quarter filling also the combined effects of disorder and interactions produce a conducting state which can be destroyed by applying a Zeeman field, resulting in a magnetic field-driven transition. We discuss the implication of our results for experiments.
Attractive Hubbard model on a honeycomb lattice: Quantum Monte Carlo study
Physical Review B, 2009
We study the attractive fermionic Hubbard model on a honeycomb lattice using determinantal quantum Monte Carlo simulations. By increasing the interaction strength U (relative to the hopping parameter t) at half-filling and zero temperature, the system undergoes a quantum phase transition at 5.0 < Uc/t < 5.1 from a semi-metal to a phase displaying simultaneously superfluid behavior and density order. Doping away from half-filling, and increasing the interaction strength at finite but low temperature T , the system always appears to be a superfluid exhibiting a crossover between a BCS and a molecular regime. These different regimes are analyzed by studying the spectral function. The formation of pairs and the emergence of phase coherence throughout the sample are studied as U is increased and T is lowered.
Quantum simulations on square and triangular Hubbard models
strength comes from the instabilities of the antiferromagnetic order (120 o-spin structure), and the nested hexagon-deformed Fermi surface with the triangular symmetry further boosts the d+id symmetry. Due to the strong competition between electronic interactions and geometric frustrations, the superconductivity and other novel features of the system equal to or above half lling requires future studies. The numerical tool we apply to study these systems is the dynamical cluster approximation with continuous-time quantum Monte Carlo as the solver. Our approach includes nonlocal correlations embedded in a mean eld host and is a most up-to-date and reliable approach in dealing with the above mentioned strongly correlated systems valid in the thermodynamic limit. Our ndings shine light on future investigations of the nature of the unconventional superconductivity in the Hubbard model. v
Quantum simulation of correlated-hopping models with fermions in optical lattices
Physical Review A, 2014
By using a modulated magnetic field in a Feshbach resonance for ultracold fermionic atoms in optical lattices, we show that it is possible to engineer a class of models usually referred to as correlated-hopping models. These models differ from the Hubbard model in exhibiting additional density-dependent interaction terms that affect the hopping processes. In addition to the spin-SU(2) symmetry, they also possess a charge-SU(2) symmetry, which opens the possibility of investigating the η-pairing mechanism for superconductivity introduced by Yang for the Hubbard model. We discuss the known solution of the model in 1D (where η states have been found in the degenerate manifold of the ground state) and show that, away from the integrable point, quantum Monte Carlo simulations at half filling predict the emergence of a phase with coexisting incommensurate spin and charge order.
Momentum dependence of the spin and charge excitations in the two dimensional Hubbard model
The low energy spin and charge excitations in the 2D Hubbard model near half filling are analyzed. The RPA spectra derived from inhomoheneous mean field textures are analyzed. Spin excitations show a commensurate peak at half filling, incommensurate peaks near half filling, and a broad background typical of a dilute Fermi liquid away from half filling. Charge excitations, near half filling, are localized near (0,0), and they occupy a small portion of the Brillouin Zone, in a way consistent with the existence of a small density of carriers, and a small Fermi surface. At higher hole densities, they fill the entire BZ, and can be understood in terms of a conventional Fermi liquid picture. The results are consistent with the observed features of the high-Tc superconductors.
The phase diagram of the square lattice bilayer Hubbard model: a variational Monte Carlo study
We investigate the phase diagram of the square lattice bilayer Hubbard model at half-filling with the variational Monte Carlo method for both the magnetic and the paramagnetic case as a function of the interlayer hopping ⊥ t and on-site Coulomb repulsion U. With this study we resolve some discrepancies in previous calculations based on the dynamical mean-field theory, and we are able to determine the nature of the phase transitions between metal, Mott insulator and band insulator. In the magnetic case we find only two phases: an anti-ferromagnetic Mott insulator at small ⊥ t for any value of U and a band insulator at large ⊥ t. At large U values we approach the Heisenberg limit. The para-magnetic phase diagram shows at small ⊥ t a metal to Mott insulator transition at moderate U values and a Mott to band insulator transition at larger U values. We also observe a re-entrant Mott insulator to metal transition and metal to band insulator transition for increasing ⊥ t in the range of < < t U t 5.5 7.5. Finally, we discuss the phase diagrams obtained in relation to findings from previous studies based on different many-body approaches.