The two orbital Hubbard model in a square lattice: a DMFT + DMRG approach (original) (raw)
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Physical Review X, 2015
Numerical results for ground state and excited state properties (energies, double occupancies, and Matsubara-axis self energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods. arXiv:1505.02290v1 [cond-mat.str-el] 9 May 2015
Physical Review B
We study the one-band Hubbard model on the honeycomb lattice using a combination of quantum Monte Carlo (QMC) simulations and static as well as dynamical mean-field theory (DMFT). This model is known to show a quantum phase transition between a Dirac semi-metal and the antiferromagnetic insulator. The aim of this article is to provide a detailed comparison between these approaches by computing static properties, notably ground-state energy, single-particle gap, double occupancy, and staggered magnetization, as well as dynamical quantities such as the single-particle spectral function. At the static mean-field level local moments cannot be generated without breaking the SU(2) spin symmetry. The DMFT approximation accounts for temporal fluctuations, thus captures both the evolution of the double occupancy and the resulting local moment formation in the paramagnetic phase. As a consequence, the DMFT approximation is found to be very accurate in the Dirac semi-metallic phase where local moment formation is present and the spin correlation length small. However, in the vicinity of the fermion quantum critical point the spin correlation length diverges and the spontaneous SU(2) symmetry breaking leads to low-lying Goldstone modes in the magnetically ordered phase. The impact of these spin fluctuations on the single-particle spectral function-waterfall features and narrow spin-polaron bands-is only visible in the lattice QMC approach.
Monte Carlo-Mean Field approach for the one band Hubbard model
Bulletin of the American Physical Society, 2015
Multiorbital model Hamiltonians are crucial to understand iron-based superconductors. We employ a recently developed "Monte Carlo-Mean Field" (MC-MF) method [1] to study single and multiband Hubbard models. The focus here is on the single band case at half filling. We start with a mean-field (MF) decomposition of the Hubbard hamiltonian and then promote the MF parameters to classical variables studied via MC simulations, while fermions are exactly diagonalized in the background of those classical variables. We present the Hubbard U vs. temperature phase diagram on large three and two dimensional clusters. Our MC-MF method can capture the nonmonotonicity of T N with U , local moment physics above T N , and the two peak behavior of specific heat, as compared with Determinantal Quantum Monte Carlo (DQMC). Results for the t − t ′ Hubbard model in two dimensions show that our approach can capture ground state and finite temperature properties reliably where DQMC fails due to sign problems. These one-band results set the stage for extending the MC-MF method to multiband Hubbard models of relevance to the Pnictide superconductors.
Local moment approach as a quantum impurity solver for the Hubbard model
Physical Review B, 2016
The local moment approach (LMA) has presented itself as a powerful semi-analytical quantum impurity solver (QIS) in the context of the dynamical mean-field theory (DMFT) for the periodic Anderson model and it correctly captures the low energy Kondo scale for the single impurity model, having excellent agreement with the Bethe ansatz and numerical renormalization group results. However, the most common correlated lattice model, the Hubbard model, has not been explored well within the LMA+DMFT framework beyond the insulating phase. Here in our work, within the framework we attempt to complete the phase diagram of the single band Hubbard model at zero temperature. Our formalism is generic to any particle filling and can be extended to finite temperature. We contrast our results with another QIS, namely the iterated perturbation theory (IPT) and show that the second spectral moment sum-rule improves better as the Hubbard interaction strength grows stronger in LMA, whereas it severely breaks down after the Mott transition in IPT. We also show that, in the metallic phase, the low-energy scaling of the spectral density leads to universality which extends to infinite frequency range at infinite correlation strength (strong-coupling). At large interaction strength, the off half-filling spectral density forms a pseudogap near the Fermi level and filling-controlled Mott transition occurs as one approaches the half-filling. Finally we study optical properties and find universal features such as absorption peak position governed by the low-energy scale and a doping independent crossing point, often dubbed as the isosbestic point in experiments.
Transport and Spectra in the Half-Filled Hubbard Model: A Dynamical Mean Field Study
International Journal of Modern Physics B, 2011
We present an improved numerical implementation of the iterated perturbation theory, for use as an impurity solver for lattice models within dynamical mean field theory (DMFT). We demonstrate higher resolution of spectral and transport features and a reduced computational expense. Using this implementation, we study the issues of scaling and universality in spectral and transport properties of the particle-hole symmetric Hubbard model within DMFT. We re-examine experimental results for pressure-dependent resistivity in Selenium doped NiS 2 and thermal hysteresis on V 2 O 3 and find qualitative agreement. A systematic study of spectral weight transfer in optical conductivity is carried out.
The one-electron Green's function of the half-filled Hubbard model on a triangular lattice
arXiv: Strongly Correlated Electrons, 2001
The one-electron density of states for the half-filled Hubbard model on a triangular lattice is studied as a function of both temperature and Hubbard U using Quantum Monte Carlo. We find three regimes: (1) a strong-coupling Mott-Hubbard regime, characterized by a gap which persists even at high temperatures; (2) a weak-coupling paramagnetic regime, characterized by the absence of a pseudogap at any finite temperature; and (3) an intermediate-coupling (spiral) spin-density-wave regime, characterized by a pseudogap which appears when U is increased beyond a critical (temperature dependent) value. The behavior of the sqrt(3) times sqrt{3} adlayer structures on fourth-group semiconductor surfaces is briefly commented upon in the light of the above discussion.
Physical Review B, 2004
In order to numerically study electron correlation effects in multi-orbital systems, we propose a new type of discrete transformation for the exchange (Hund's coupling) and pair-hopping interactions to be used in the dynamical mean field theory + quantum Monte Carlo method. The transformation, which is real and exact, turns out to suppress the sign problem in a wide parameter region including non-half-filled bands. This enables us to obtain the dominant pairing symmetry in the double-orbital Hubbard model, which shows that the spin-triplet, orbital-antisymmetric pairing that exploits Hund's coupling is stable in a wide region of the band filling.
Physical Review B, 2008
We investigate the Hubbard model on the triangular lattice at half-filling using the dynamical cluster approximation (DCA) and dual fermion (DF) methods in combination with continuous-time quantum Monte carlo (CT QMC) and semiclassical approximation (SCA) methods. We study the one-particle properties and nearest-neighbor spin correlations using the DCA method. We calculate the spectral functions using the CT QMC and SCA methods. The spectral function in the SCA and obtained by analytic continuation of the Pade approximation in CT QMC are in good agreement. We determine the metal-insulator transition (MIT) and the hysteresis associated with a first-order transition in the double occupancy and nearest-neighbor spin correlation functions as a function of temperature. As a further check, we employ the DF method and discuss the advantages and limitation of the dynamical mean field theory (DMFT), DCA and recently developed DF methods by comparing Green's functions. We find an enhancement of antiferromagnetic (AF) correlations and provide evidence for magnetically ordered phases by calculating the spin susceptibility.
Quantum Monte Carlo study of the two-dimensional fermion Hubbard model
We report large scale determinant quantum Monte Carlo calculations of the effective bandwidth, momentum distribution, and magnetic correlations of the square lattice fermion Hubbard Hamiltonian at half-filling. The sharp Fermi surface of the noninteracting limit is significantly broadened by the electronic correlations but retains signatures of the approach to the edges of the first Brillouin zone as the density increases. Finite-size scaling of simulations on large lattices allows us to extract the interaction dependence of the antiferromagnetic order parameter, exhibiting its evolution from weak-coupling to the strong-coupling Heisenberg limit. Our lattices provide improved resolution of the Green’s function in momentum space, allowing a more quantitative comparison with time-of-flight optical lattice experiments.