Backflow correlations in the Hubbard model: An efficient tool for the study of the metal-insulator transition and the large-U limit (original) (raw)
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Metal-insulator transition in the one-dimensional SUÑNÖ Hubbard model
1999
We investigate the metal-insulator transition of the one-dimensional SU(N) Hubbard model for repulsive interaction. Using the bosonization approach a Mott transition in the charge sector at half filling (k F ϭ/Na 0) is conjectured for NϾ2. Expressions for the charge and spin velocities as well as for the Luttingerliquid parameters and some correlation functions are given. The theoretical predictions are compared with numerical results obtained with an improved zero-temperature quantum Monte Carlo approach. The method used is a generalized Green's function Monte Carlo scheme in which the stochastic time evolution is partially integrated out. Very accurate results for the gaps, velocities, and Luttinger-liquid parameters as a function of the Coulomb interaction U are given for the cases Nϭ3 and Nϭ4. Our results strongly support the existence of a Mott-Hubbard transition at a nonzero value of the Coulomb interaction. We find U c ϳ2.2 for Nϭ3 and U c ϳ2.8 for Nϭ4. ͓S0163-1829͑99͒00728-6͔
Mott metal-insulator transition in the half-filled Hubbard model on the triangular lattice
Physical Review B, 2001
We investigate the metal-insulator transition in the half-filled Hubbard model on a two-dimensional triangular lattice using both the Kotliar-Ruckenstein slave-boson technique, and exact numerical diagonalization of finite clusters. Contrary to the case of the square lattice, where the perfect nesting of the Fermi surface leads to a metal-insulator transition at arbitrarily small values of U , always accompanied by antiferromagnetic ordering, on the triangular lattice, due to the lack of perfect nesting, the transition takes place at a finite value of U , and frustration induces a nontrivial competition among different magnetic phases. Indeed, within the mean-field approximation in the slave-boson approach, as the interaction grows the paramagnetic metal turns into a metallic phase with incommensurate spiral ordering. Increasing further the interaction, a linear spin-densitywave is stabilized, and finally for strong coupling the latter phase undergoes a first-order transition towards an antiferromagnetic insulator. No trace of the intermediate phases is instead seen in the exact diagonalization results, indicating a transition between a paramagnetic metal and an antiferromagnetic insulator. 71.10.Fd, 71.30.+h, 75.10.Lp
Journal of Magnetism and Magnetic Materials, 1995
We investigate the metal-insulator transition of the one-dimensional SU(N) Hubbard model for repulsive interaction. Using the bosonization approach a Mott transition in the charge sector at half-filling (kF =π/N a0) is conjectured for N > 2. Expressions for the charge and spin velocities as well as for the Luttinger liquid parameters and some correlation functions are given. The theoretical predictions are compared with numerical results obtained with an improved zero-temperature quantum Monte Carlo approach. The method used is a generalized Green's function Monte Carlo scheme in which the stochastic time evolution is partially integrated out. Very accurate results for the gaps, velocities, and Luttinger liquid parameters as a function of the Coulomb interaction U are given for the cases N = 3 and N = 4. Our results strongly support the existence of a Mott-Hubbard transition at a non-zero value of the Coulomb interaction. We find Uc ∼ 2.2 for N = 3 and Uc ∼ 2.8 for N = 4.
Europhysics Letters (EPL), 2000
The Mott-Hubbard transition is studied in the context of the two-dimensional Hubbard model. Analytical calculations show the existence of a critical value Uc of the potential strength which separates a paramagnetic metallic phase from a paramagnetic insulating phase. Calculations of the density of states and double occupancy show that the ground state in the insulating phase contains always a small fraction of empty and doubly occupied sites. The structure of the ground state is studied by considering the probability amplitude of intersite hopping. The results indicate that the ground state of the Mott insulator is characterized by a local antiferromagnetic order; the electrons keep some mobility, but this mobility must be compatible with the local ordering. The vanishing of some intersite probability amplitudes at U = Uc puts a constrain on the electron mobility. It is suggested that such quantities might be taken as the quantities which control the order in the insulating phase.
Finite Doping Signatures of the Mott Transition in the Two-Dimensional Hubbard Model
Physical Review Letters, 2010
Experiments on layered materials call for a study of the influence of short-range spin correlations on the Mott transition. To this end, we solve the cluster dynamical mean-field equations for the Hubbard model on a plaquette with continuous-time quantum Monte Carlo. The normal state phase diagram as a function of temperature T , interaction strength U and filling n reveals that upon increasing n towards the insulator, there is a surface of first-order transition between two metals at non-zero doping. For T above the critical end line there is a maximum in scattering rate.
Metal-insulator transition and charge ordering in the extended Hubbard model at one-quarter filling
Physical Review B, 2002
We study with exact diagonalization the zero temperature properties of the quarter-filled extended Hubbard model on a square lattice. We find that increasing the ratio of the intersite Coulomb repulsion, V , to the band width drives the system from a metal to a charge ordered insulator. The evolution of the optical conductivity spectrum with increasing V is compared to the observed optical conductivity of several layered molecular crystals with the θ and β ′′ crystal structures. PACS numbers: 71.27+a, 71.30+h Charge ordering in strongly correlated electron systems is currently under intense investigation. Charge ordering is relevant to a broad range of materials including the cuprates[1], manganates[2], magnetite[3], vanadium oxides[4], and the Bechgaard salts [5]. The θ and β ′′ types of layered molecular crystals based on molecules such as BEDT-TTF [= bisethylenedithio-tetrathiafulvalene] [6], display charge ordering, metallic, and superconducting phases close to each other [7]. Charge ordering driven by a strong inter-site Coulomb repulsion is possible in crystals with the θ and β ′′ arrangements of BEDT-TTF molecules because their bands are quarter-filled with holes, in contrast to the well studied κ-type, for which strong dimerization of the molecules lead to a halffilled band . The θ-type crystals undergo a transition from a metal to a charge ordered insulator as the temperature, pressure, uniaxial stress, or anion is varied . Furthermore, the metallic phase exhibits features characteristic of a strongly correlated system. In particular, the optical conductivity spectra display a broad mid-infrared band and a near absence of a Drude-like peak . This is in contrast to conventional metals, for which the total spectral weight is dominated by a Drude peak.
Continuous evolution of the 2D Hubbard model from an insulator to a metal
Journal of Physics and Chemistry of Solids, 1995
We present Quantum-Monte-Carlo results for the momentum and frequency dependent spectral weight A(k; !) showing the evolution from insulating to metallic behavior in the two-dimensional Hubbard model. As observed in recent photoemission experiments for cuprates, in both undoped and doped cases the electronic excitations display two rather similar general features, i.e. a quasiparticle (QP)-like dispersive band of small width of the order of the exchange interaction J and a broad valence-and conduction-band background. Arguments for one and the same manybody physics namely the continuous reduction of the spin-spin correlation length and related changes in the QP-spin correlations behind the continuous evolution to the metallic QP dispersion are given. 3 J J
The metal–insulator transition in the paramagnetic Hubbard Model
Physica B: Condensed Matter, 2008
We study the Mott transition in the Hubbard Model within the dynamical mean field theory (DMFT) approach. The DMFT equations are solved using the density matrix renormalization group technique. The densities of states for the half-filled and heavily doped cases are shown. The full phase diagram is also presented.