Hubbard Model In Infinite Dimensions Research Articles

Long-term memory magnetic correlations in the Hubbard model: A dynamical mean-field theory analysis

We investigate the onset of a not-decaying asymptotic behavior of temporal magnetic correlations in the Hubbard model in infinite dimensions. This long-term memory feature of dynamical spin correlations can be precisely quantified by computing the difference between the zero-frequency limit of the Kubo susceptibility and the corresponding static isothermal one. Here, we present a procedure for reliably evaluating this difference starting from imaginary time-axis data, and apply it to the testbed case of the Mott-Hubbard metal-insulator transition (MIT). At low temperatures, we find long-term memory effects in the entire Mott regime, abruptly ending at the first order MIT. This directly reflects the underlying local moment physics and the associated degeneracy in the many-electron spectrum. At higher temperatures, a more gradual onset of an infinitely-long time-decay of magnetic correlations occurs in the crossover regime, not too far from the Widom line emerging from the critical point of the MIT. Our work has relevant algorithmic implications for the analytical continuation of dynamical susceptibilities in strongly correlated regimes and offers a new perspective for unveiling fundamental properties of the many-particle spectrum of the problem under scrutiny.

Foundations of variational discrete action theory

A new variational theory is proposed, based on the sequential product density matrix (SPD) ansatz, which is characterized by an integer and monotonically approaches the exact solution. The authors introduce the discrete action theory to evaluate the SPD, yielding the variational discrete action theory (VDAT). VDAT can be exactly evaluated for the multiband Anderson impurity model and the multiband Hubbard model in infinite dimensions. This provides an unprecedented combination of efficiency and precision within a single framework.

Fully algebraic and self-consistent effective dynamics in a static quantum embedding

Quantum embedding approaches involve the self-consistent optimization of a local fragment of a strongly correlated system, entangled with the wider environment. The `energy-weighted' density matrix embedding theory (EwDMET) was established recently as a way to systematically control the resolution of the fragment-environment coupling, and allow for true quantum fluctuations over this boundary to be self-consistently optimized within a fully static framework. In this work, we reformulate the algorithm to ensure that EwDMET can be considered equivalent to an optimal and rigorous truncation of the self-consistent dynamics of dynamical mean-field theory (DMFT). A practical limitation of these quantum embedding approaches is often a numerical fitting of a self-consistent object defining the quantum effects. However, we show here that in this formulation, all numerical fitting steps can be entirely circumvented, via an effective Dyson equation in the space of truncated dynamics. This provides a robust and analytic self-consistency for the method, and an ability to systematically and rigorously converge to DMFT from a static, wave function perspective. We demonstrate that this improved approach can solve the correlated dynamics and phase transitions of the Bethe lattice Hubbard model in infinite dimensions, as well as one- and two-dimensional Hubbard models where we clearly show the benefits of this rapidly convergent basis for correlation-driven fluctuations. This systematically truncated description of the effective dynamics of the problem also allows access to quantities such as Fermi liquid parameters and renormalized dynamics, and demonstrates a numerically efficient, systematic convergence to the zero-temperature dynamical mean-field theory limit.

Extremely correlated Fermi liquid theory of the t-J model in 2 dimensions: low energy properties

Low energy properties of the metallic state of the two-dimensional t-J model are presented for second neighbor hopping with hole-doping () and electron-doping (), with various superexchange energy J. We use a closed set of equations for the Greens functions obtained from the extremely correlated Fermi liquid theory. These equations reproduce the known low energies features of the large U Hubbard model in infinite dimensions. The density and temperature dependent quasiparticle weight, decay rate and the peak spectral heights over the Brillouin zone are calculated. We also calculate the resistivity, Hall conductivity, Hall number and cotangent Hall angle. The spectral features display high thermal sensitivity at modest T for density , implying a suppression of the effective Fermi-liquid temperature by two orders of magnitude relative to the bare bandwidth. The cotangent Hall angle exhibits a T2 behavior at low T, followed by an interesting kink at higher T. The Hall number exhibits strong renormalization due to correlations. Flipping the sign of changes the curvature of the resistivity versus T curves between convex and concave. Our results provide a natural route for understanding the observed difference in the temperature dependent resistivity of strongly correlated electron-doped and hole-doped matter.

Superconductivity in the two-band Hubbard model

We study the two-band Hubbard model in infinite dimensions by solving the dynamical mean-field equations with a strong coupling continuous-time quantum Monte Carlo method and show that an $s$-wave superconducting state can be stabilized in the repulsively interacting case. We discuss how this superconducting state competes with the metallic and paired Mott states. The effects of the Hund coupling and crystalline electric field are also addressed.

Estimate of the phase transition line in the infinite-dimensional Hubbard model

We consider a Mott transition of the Hubbard model in infinite dimensions. The dynamical meanfield theory is employed in combination with a continuous-time quantum Monte Carlo (CTQMC) method for an accurate description at low temperatures. From the double occupancy and the energy density, which are directly measured from the CTQMC method, we construct the phase diagram. We pay particular attention to the construction of the first-order phase transition line (PTL) in the coexistence region of metallic and insulating phases. The resulting PTL is found to exhibit reasonable agreement with earlier finite-temperature results. We also show by a systematic inclusion of low-temperature data that the PTL, which is achieved independently of the previous zero-temperature results, approaches monotonically the transition point from earlier zerotemperature studies.

Optimal ramp shapes for the fermionic Hubbard model in infinite dimensions

We use nonequilibrium dynamical mean field theory and a real-time diagrammatic impurity solver to study the heating associated with time-dependent changes of the interaction in a fermionic Hubbard model. Optimal ramp shapes $U(t)$ which minimize the excitation energy are determined for a noninteracting initial state and an infinitesimal change of the interaction strength. For ramp times of a few inverse hoppings, these optimal $U(t)$ are strongly oscillating with a frequency determined by the bandwidth. We show that the scaled versions of the optimized ramps yield substantially lower temperatures than linear ramps even for final interaction values comparable to the bandwidth. The relaxation of the system after the ramp and its dependence on the ramp shape are also addressed.

Generic susceptibilities of the half-filled Hubbard model in infinite dimensions

(Dated: April 3, 2009)Around a metal-to-insulator transition driven by repulsive interaction (Mott transition) the singleparticle excitations and the collective excitations are equally important. Here we present results forthe generic susceptibilities at zero temperature in the half-filled Hubbard model in infinite dimen-sions. Profiting from the high resolution of dynamic density-matrix renormalization at all energies,results for the charge, spin and Cooper-pair susceptibilities in the metallic and the insulating phaseare computed. In the insulating phase, an almost saturated local magnetic moment appears. In themetallic phase a pronounced low-energy peak is found in the spin response. It is the precursor ofthe magnetic moment in the insulator.

Local-Ansatz Approach with Momentum Dependent Variational Parameters to Correlated Electron Systems

A new wavefunction which improves the Gutzwiller-type local ansatz method has been proposed to describe the correlated electron system. The ground-state energy, double occupation number, momentum distribution function, and quasiparticle weight have been calculated for the half-filled band Hubbard model in infinite dimensions. It is shown that the new wavefunction improves the local-ansatz approach (LA) proposed by Stollhoff and Fulde. Especially, calculated momentum distribution functions show a reasonable momentum dependence. The result qualitatively differs from those obtained by the LA and the Gutzwiller wavefunction. Furthermore, the present approach combined with the projection operator method CPA is shown to describe quantitatively the excitation spectra in the insulator regime as well as the critical Coulomb interactions for a gap formation in infinite dimensions.

Random dispersion approximation for the Hubbard model

We use the Random Dispersion Approximation (RDA) to study the Mott-Hubbard transition in the Hubbard model at half band filling. The RDA becomes exact for the Hubbard model in infinite dimensions. We implement the RDA on finite chains and employ the Lanczos exact diagonalization method in real space to calculate the ground-state energy, the average double occupancy, the charge gap, the momentum distribution, and the quasi-particle weight. We find a satisfactory agreement with perturbative results in the weak- and strong-coupling limits. A straightforward extrapolation of the RDA data for L ≤ 14 lattice results in a continuous Mott-Hubbard transition at Uc ≈ W.W e discuss the signif icance of a possible signature of a coexistence region between insulating and metallic ground states in the RDA that would correspond to the scenario of a discontinuous Mott-Hubbard transition as found in numerical investigations of the Dynamical Mean-Field Theory for the Hubbard model.

Trionic phase of ultracold fermions in an optical lattice: A variational study

To investigate ultracold fermionic atoms of three internal states (colors) in an optical lattice, subject to strong attractive interaction, we study the attractive three-color Hubbard model in infinite dimensions by using a variational approach. We find a quantum phase transition between a weak-coupling superconducting phase and a strong-coupling trionic phase where groups of three atoms are bound to a composite fermion. We show how the Gutzwiller variational theory can be reformulated in terms of an effective field theory with three-body interactions and how this effective field theory can be solved exactly in infinite dimensions by using the methods of dynamical mean field theory.

Phase diagrams of the two-orbital Hubbard model with different bandwidths

We investigate the two-orbital Hubbard model in infinite dimensions by means of the self-energy functional method. By calculating the entropy, susceptibility, and quasi particle weight at zero temperature, we determine the phase diagram for the system with same and different bandwidths, which is compared with that obtained recently. It is clarified that orbital fluctuations play a key role in controlling the nature of the Mott transitions in the system.

Brueckner–Goldstone perturbation theory for the half-filled Hubbard model in infinitedimensions

We use Brueckner–Goldstone perturbation theory to calculate the ground-state energy ofthe half-filled Hubbard model in infinite dimensions up to fourth order in the Hubbardinteraction. We obtain the momentum distribution as a functional derivative of theground-state energy with respect to the bare dispersion relation. The resultingexpressions agree with those from Rayleigh–Schrödinger perturbation theory. Ourresults for the momentum distribution and the quasi-particle weight agree verywell with those obtained earlier from Feynman–Dyson perturbation theory forthe single-particle self-energy. We give the correct fourth-order coefficient in theground-state energy which was not calculated accurately enough from Feynman–Dysontheory due to the insufficient accuracy of the data for the self-energy, and find agood agreement with recent estimates from quantum Monte Carlo calculations.

Phase diagram for the exciton Mott transition in infinite-dimensional electron–hole systems

To understand the essence of the exciton Mott transition in three-dimensional electron–hole systems, the metal–insulator transition is studied for a two-band Hubbard model in infinite dimensions with interactions of electron–electron (hole–hole) repulsion U and electron–hole attraction - U ′ . By using the dynamical mean-field theory, the phase diagram in the U– U ′ plane is obtained (which is exact in infinite dimensions) assuming that electron–hole pairs do not condense. When both electron and hole bands are half-filled, two types of insulating states appear: the Mott–Hubbard insulator for U > U ′ and the biexciton-like insulator for U < U ′ . Even when away from half-filling, we find the phase transition between the exciton- or biexciton-like insulator and a metallic state. This transition can be assigned to the exciton Mott transition, whereas the Mott–Hubbard transition is absent.

Fourth-order perturbation theory for the half-filled Hubbard model in infinite dimensions

We calculate the zero-temperature self-energy to fourth-order perturbation theory in the Hubbard interaction $U$ for the half-filled Hubbard model in infinite dimensions. For the Bethe lattice with bare bandwidth $W$, we compare our perturbative results for the self-energy, the single-particle density of states, and the momentum distribution to those from approximate analytical and numerical studies of the model. Results for the density of states from perturbation theory at $U/W=0.4$ agree very well with those from the Dynamical Mean-Field Theory treated with the Fixed-Energy Exact Diagonalization and with the Dynamical Density-Matrix Renormalization Group. In contrast, our results reveal the limited resolution of the Numerical Renormalization Group approach in treating the Hubbard bands. The momentum distributions from all approximate studies of the model are very similar in the regime where perturbation theory is applicable, $U/W \le 0.6$. Iterated Perturbation Theory overestimates the quasiparticle weight above such moderate interaction strengths.

Mott transition in the multi-band Hubbard model in infinite dimensions

The Mott metal–insulator transition in the multi-band Hubbard model in infinite dimensions is studied by using the linearized dynamical mean-field theory. The critical interaction U c is obtained analytically. For the symmetric case and for orbital degeneracy M we find U c =(4M+2) L 2 where L 2 is the second moment of the non-interacting density of states. We also derive an analytical expression for the discontinuity of the chemical potential μ( n) at the filling n= M for U> U c. The findings are in good agreement with numerical results obtained from the exact diagonalization method.

Effect of Direct Transfer on Critical Behaviour of Mott Transition in the Two-Band Hubbard Model

The Mott metal–insulator transition in the two-band Hubbard model in infinite dimensions is studied by using the linearized dynamical mean-field theory. The discontinuity in the chemical potential for the change from hole to electron doping is calculated analytically as a function of the on-site Coulomb interaction U , and the charge-transfer energy Δ between the d - and p -orbitals, transfer integrals t p d , t p p , t d d between p – d , p – p , and d – d sites respectively. The critical behaviour of the quasiparticle weight is also obtained analytically.

Magnetism and Superconductivity in a Two-band Hubbard Model in Infinite Dimensions

We study a two-band Hubbard model using the dynamical mean-field theory combined with the exact diagonalization method. At the electron density $n=2$, a transition from a band-insulator to a correlated semimetal occurs when the on-site Coulomb interaction $U$ is varied for a fixed value of the charge-transfer energy $\Delta$. At low temperature, the correlated semimetal shows ferromagnetism or superconductivity. With increasing doping $|n-2|$, the ferromagnetic transition temperature rapidly decreases and finally becomes zero at a critical value of $n$. The second-order phase transition occurs at high temperature, while a phase separation of ferromagnetic and paramagnetic states takes place at low temperature. The superconducting transition temperature gradually decreases and finally becomes zero near $n=1$ ($n=3$) where the system is Mott insulator which shows antiferromagnetism at low temperature.

Exact theory for electronic Raman scattering of correlated materials in infinite dimensions

The numerically exact solution for nonresonant B1g Raman scattering is presented for the half-filled Hubbard model in infinite dimensions. This solution illustrates the modifications of the Raman response (in a system tuned through the quantum-critical point of a metal-insulator transition) due to Fermi-liquid properties in the metallic phase. In the insulating phase, we recover the predicted universal behavior, while we find the Raman response is quite anomalous on the metallic side of the transition. Our calculated results are similar to those measured in FeSi, SmB6, and underdoped cuprates.

Critical Behaviour near the Mott Metal–Insulator Transition in a Two-Band Hubbard Model

The Mott metal-insulator transition in the two-band Hubbard model in infinite dimensions is studied by using the linearized dynamical mean-field theory. The discontinuity in the chemical potential for the change from hole to electron doping is calculated analytically as a function of the on-site Coulomb interaction $U$ at the $d$-orbital and the charge-transfer energy $\Delta$ between the $d$- and $p$-orbitals. Critical behaviour of the quasiparticle weight is also obtained analytically as a function of $U$ and $\Delta$. The analytic results are in good agreement with the numerical results of the exact diagonalization method.