Mean-field Study Research Articles

Cellular Dynamical Mean Field Study on Two-Orbital Hubbard Model with Different Bandwidths

We study spin and orbital correlations in the two-orbital Hubbard model with different bandwidths at quarter filling by means of the cellular dynamical mean field theory combined with the noncrossing approximation. We show that the ferromagnetic-antiferro-orbital insulating state is stabilized by the Hund's coupling in the system with the same bandwidths and the antiferromagnetic-ferro-orbital insulating state appears when the difference of bandwidths is quite large. We find that the competition between the two states occurs in the intermediate region and this competition gives rise to the strongly renormalized metallic state.

Slave-boson mean-field study of the dimensional crossover in Sr2RuO4

The anomalous temperature dependence of the c-axis resistivity of Sr2RuO4 is analyzed under the viewpoint of a dimensional crossover which occurs from a lattice of perpendicular one-dimensional chains, belonging to different Ru-4d-orbitals, to a two-dimensional system induced by weak inter-orbital hybridization. This system is described by a two-orbital Hubbard model which is treated within a slave-boson mean-field approach to take correlation effects, such as the spin-charge separation, into account. We obtain the emergence of quasiparticle states at low temperature, a result which can be used to discuss the evolution of the spectral density and the c-axis transport within a tunneling approach. For the latter, a crossover between the low- and high-temperature regime is found in qualitative agreement with experimental observations.

Neutron star cooling: A challenge to the nuclear mean field

The two recent density-dependent versions of the finite-range M3Y interaction (CDM3Y$n$ and M3Y-P$n$) have been probed against the bulk properties of asymmetric nuclear matter (NM) in the nonrelativistic Hartree Fock (HF) formalism. The same HF study has also been done with the famous Skyrme (SLy4) and Gogny (D1S and D1N) interactions which were well tested in the nuclear structure calculations. Our HF results are compared with those given by other many-body calculations like the Dirac-Brueckner Hartree-Fock approach or ab-initio variational calculation using free nucleon-nucleon interaction, and by both the nonrelativistic and relativistic mean-field studies using different model parameters. Although the two considered density-dependent versions of the M3Y interaction were proven to be quite realistic in the nuclear structure or reaction studies, they give two distinct behaviors of the NM symmetry energy at high densities, like the Asy-soft and Asy-stiff scenarios found earlier with other mean-field interactions. As a consequence, we obtain two different behaviors of the proton fraction in the $\beta$-equilibrium which in turn can imply two drastically different mechanisms for the neutron star cooling. While some preference of the Asy-stiff scenario was found based on predictions of the latest microscopic many-body calculations or empirical NM pressure and isospin diffusion data deduced from heavy-ion collisions, a consistent mean-field description of nuclear structure database is more often given by some Asy-soft type interaction like the Gogny or M3Y-P$n$ ones. Such a dilemma poses an interesting challenge to the modern mean-field approaches.

Magnetism and orbital ordering in an interacting three-band model: A dynamical mean-field study

Single-site dynamical mean-field theory is used to determine the magnetic and orbital-ordering phase diagram for a model of electrons moving on a lattice with three orbital states per site and with the fully rotationally invariant Slater-Kanamori on-site interactions. The model captures important aspects of the physics of transition-metal oxides with partially filled ${t}_{2g}$ shells and of electron-doped ${\text{C}}_{60}$. We introduce an unbiased, computationally simple, and inexpensive method for estimating the presence of two-sublattice order, determine the regimes in which spatially uniform and two-sublattice spin and orbital orderings are present and give physical arguments for the origins of the different phases. Guidelines are determined for optimizing the presence of ferromagnetism, which may be desirable in applications.

Momentum-sector-selective metal-insulator transition in the eight-site dynamical mean-field approximation to the Hubbard model in two dimensions

We explore the momentum-sector-selective metal-insulator transitions recently found in the eight-site dynamical cluster approximation to the two-dimensional Hubbard model. The phase diagram in the space of interaction and second-neighbor hopping is established. The initial transitions from Fermi-liquid-like to sector-selective phases are found to be of second order, caused by the continuous opening of an energy gap whereas the other transitions are found to be of first order. In the sector-selective phase the Fermi surface regions which are not gapped are found to have a non-Fermi-liquid self-energy. We demonstrate that the phenomenon is not caused by the Van Hove divergence in the density of states. The sector-selective and insulating phases are characterized by a cluster spin-correlation function that is strongly peaked at the commensurate antiferromagnetic wave vector $(\ensuremath{\pi},\ensuremath{\pi})$ but the model has no nematic instability. Comparison to dynamical mean-field studies on smaller clusters is made.

Finite-temperature exact diagonalization cluster dynamical mean-field study of the two-dimensional Hubbard model: Pseudogap, non-Fermi-liquid behavior, and particle-hole asymmetry

The effect of doping in the two-dimensional Hubbard model is studied within finite-temperature exact diagonalization combined with cluster dynamical mean-field theory. By employing a mixed basis involving cluster sites and bath molecular orbitals for the projection of the lattice Green's function onto $2\ifmmode\times\else\texttimes\fi{}2$ clusters, a considerably more accurate description of the low-frequency properties of the self-energy is achieved than in a pure site picture. To evaluate the phase diagram, the transition from Fermi-liquid to non-Fermi-liquid behavior for decreasing hole doping is studied as a function of Coulomb energy, next-nearest-neighbor hopping, and temperature. The self-energy component ${\ensuremath{\Sigma}}_{X}$ associated with $X=(\ensuremath{\pi},0)$ is shown to develop a collective mode above ${E}_{F}$, whose energy and strength exhibits a distinct dispersion with doping. This low-energy excitation gives rise to non-Fermi-liquid behavior as the hole doping decreases below a critical value ${\ensuremath{\delta}}_{c}$, and to an increasing particle-hole asymmetry, in agreement with recent photoemission data. This behavior is consistent with the removal of spectral weight from electron states above ${E}_{F}$ and the opening of a pseudogap, which increases with decreasing doping. The phase diagram reveals that ${\ensuremath{\delta}}_{c}\ensuremath{\approx}0.15\dots{}0.20$ for various system parameters. For electron doping, the collective mode of ${\ensuremath{\Sigma}}_{X}(\ensuremath{\omega})$ and the concomitant pseudogap are located below the Fermi energy, which is consistent with the removal of spectral weight from the hole states just below ${E}_{F}$. The critical doping, which marks the onset of non-Fermi-liquid behavior, is systematically smaller than for hole doping.

Mean-Field Studies of a Mixed Spin-3/2 and Spin-2 and a Mixed Spin-3/2 and Spin-5/2 Ising System with Different Anisotropies

The magnetic properties of a mixed spin-3/2 and spin-2 and a mixed spin-3/2 and spin-5/2 Ising ferromagnetic system with different anisotropies are studied by means of mean-field theory (MFT). The dependence of the phase diagram on single-ion anisotropy strengths is studied too. In the mixed spin-3/2 and spin-2 Ising model, besides the second-order phase transition, the first order-disorder phase transition and the tricritical line are found. In the mixed spin-3/2 and spin-5/2 Ising model, there is no first-order transition and tricritical line.

Dynamical mean field study of the Dirac liquid

Renormalization is one of the basic notions of condensed matter physics. Based on the concept of renormalization, the Landau’s Fermi liquid theory has been able to explain, why despite the presence of Coulomb interactions, the free electron theory works so well for simple metals with extended Fermi surface (FS). The recent synthesis of graphene has provided the condensed matter physicists with a low energy laboratory of Dirac fermions where instead of a FS, one has two Fermi points. Many exciting phenomena in graphene can be successfully interpreted in terms of free Dirac electrons. In this paper, employing dynamical mean field theory (DMFT), we show that an interacting Dirac sea is essentially an effective free Dirac theory. This observation suggests the notion of Dirac liquid as a fixed point of interacting 2 + 1 dimensional Dirac fermions. We find one more fixed point at strong interactions describing a Mott insulating state, and address the nature of semi-metal to insulator (SMIT) transition in this system.

Spatial fluctuations of spin and orbital in two-orbital Hubbard model: cluster dynamical mean field study

We investigate the single-particle dynamics and magnetic properties in the two-orbital Hubbard model on the square lattice at quarter filling by using a cluster extension of dynamical mean field theory. We find that the Fermi-liquid state is stabilized up to the large intra- and inter-orbital interactions in the symmetric case without Hund's coupling. It is clarified that the Hund's coupling enhances the antiferro-orbital fluctuations, which gives rise to the pseudo gap behavior in the single-particle excitations. We also find that the Hund's coupling with intermediate strength causes the competition between the Fermi-liquid formation and the antiferro-orbital fluctuations, resulting in the nonmonotonous temperature dependence in the single-particle dynamics.

Kinks in the Electronic Specific Heat

We find that the heat capacity of a strongly correlated metal presents striking changes with respect to Landau Fermi-liquid theory. In contrast with normal metals, where the electronic specific heat is linear at low temperature (with a T3 term as a leading correction), a dynamical mean-field study of the correlated Hubbard model reveals a clear kink in the temperature dependence, marking a rapid change from a low-temperature linear behavior and a second linear regime with a reduced slope. Experiments on LiV2O4 support our findings, implying that correlated materials are more resistive to cooling at low T than expected from the intermediate temperature behavior.

Feshbach-Einstein Condensates

We investigate the phase diagram of a two-species Bose-Hubbard model describing atoms and molecules on a lattice, interacting via a Feshbach resonance. We identify a region where the system exhibits an exotic super-Mott phase and regions with phases characterized by atomic and/or molecular condensates. Our approach is based on a recently developed exact quantum Monte Carlo algorithm: the stochastic Green function algorithm with tunable directionality. We confirm some of the results predicted by mean-field studies, but we also find disagreement with these studies. In particular, we find a phase with an atomic but no molecular condensate, which is missing in all mean-field phase diagrams.

The Fermi surface reconstruction in stripe phases of cuprates

Mean-field study of the stripe structures is conducted for a hole-doped Hubbard model. For bond-directed stripes, the Fermi surface consists of segments of an open surface and the boundaries of the hole pockets which appear in the diagonal region of momenta under certain conditions. Segments of the first type are due to one-dimensional bands of states localized on the domain walls. The relation of bands to the doping and temperature dependences of the Hall constant is discussed. In connection with the observation of quantum magnetic oscillations, a systematic search for the electron pockets has been carried out. It is shown that the formation of such pockets in bilayer models is quite possible.

Cluster dynamical mean-field study of the Hubbard model on a 3D frustrated hyperkagome lattice

We study the Hubbard model on a geometrically-frustrated hyperkagome lattice by a cluster extension of the dynamical mean field theory. We calculate the temperature (T) dependences of the specific heat (C) and the spin-lattice relaxation time (T1) in correlated metallic region. C/T shows a peak at T = Tp1 and rapidly decreases as T → 0. On the other hand, 1/T1T has a peak at a higher temperature Tp2 than Tp1, and largely decreases below Tp2, followed by the Korringa law 1/T1 ∝ T as T → 0. Both peak temperatures are suppressed and the peaks become sharper as electron correlation is increased. These behaviors originate from strong renormalization of the energy scales in the peculiar electronic structure in this frustrated system; a pseudo-gap like feature, the van-Hove singularity, and the flat band. The results are discussed in comparison with the experimental data in the hyperkagome material, Na4Ir3O8.

Static and dynamic glass–glass transitions: A mean-field study

The behavior of a family of mean-field glass models is reviewed. The models are analysed by means of a Langevin-based approach to the dynamics and a replica theory computation of the thermodynamics. We focus on the phase diagram of a particular model case, where glass-to-glass transitions occur between phases with a different number of characteristic time-scales for the relaxation processes. The appearance of Johari-Goldstein processes as collective reorganizations of sets of fast processes is discussed.

Spin Freezing Transition and Non-Fermi-Liquid Self-Energy in a Three-Orbital Model

A single-site dynamical mean-field study of a three band model with the rotationally invariant interactions appropriate to the t_(2g) levels of a transition metal oxide reveals a quantum phase transition between a paramagnetic metallic phase and an incoherent metallic phase with frozen moments. The Mott transitions occurring at electron densities n=2, 3 per site take place inside the frozen moment phase. The critical line separating the two phases is characterized by a self-energy with the frequency dependence Sigma(omega) approximately sqrt[omega] and a broad quantum critical regime. The findings are discussed in the context of the power law observed in the optical conductivity of SrRuO3.

Interplay of charge density wave and spin density wave in high- Tc superconductors

We present a mean-field theory theoretical model study for the coexistence of the two strongly interacting charge density wave (CDW) and spin density wave (SDW) for high- T c cuprates in the underdoped region before the onset of the superconductivity in the system. The analytic expressions for the temperature dependence of the CDW and SDW order parameters are derived and solved self-consistently. Their interplay is studied by varying their respective coupling constants. It is observed that in the interplay region both the gap parameters exhibit very strong dependence of their gap values for the coupling constants. Further, the electronic density of states (DOS) for the conduction electrons, which represents the scanning tunneling data, show two gap parameters in the interplay region from these experimental data. Our model can help to determine separately the CDW and SDW parameters.

Interplay of metamagnetic and structural transitions in Ca2-xSrxRuO4

Metamagnetism in layered ruthenates has been interpreted as a novel kind of quantum critical behavior. In an external magnetic field, Ca2-xSrxRuO4 undergoes a metamagnetic transition accompanied by a pronounced magnetostriction effect. In this paper we present a mean-field study for a microscopic model that naturally reproduces the key features of this system. The phase diagram calculated is equivalent to the experimental T-x phase diagram. The presented model also gives a good basis to discuss the critical metamagnetic behavior measured in the system.

Quantum Monte Carlo study of a two-species bosonic Hubbard model

We consider a two-species hard-core boson Hubbard model for a supersolid, where the two types of bosons represent vacancies and interstitials doped into a commensurate crystal. The on-site inter-species interaction may create bound states of vacancies and interstitials facilitating vacancy condensation at lower energies than in a single-species model, as suggested in an earlier mean field study. Here we carry out quantum Monte Carlo simulation to study possible supersolid phases of the model, corresponding to superfluid phases of the vacancies or interstitials. At low temperatures, we find three distinct superfluid phases. The extent of the phases and the nature of the phase transitions are discussed in comparison to mean-field theory.

Mean-field study of the heavy-fermion metamagnetic transition

We investigate the evolution of the heavy-fermion ground state under application of a strong external magnetic field. We present a richer version of the usual hybridization mean-field theory that allows for hybridization in both the singlet and triplet channels and incorporates a self-consistent Weiss field. We show that for a magnetic field strength ${B}^{*}$, a filling-dependent fraction of the zero-field hybridization gap, the spin up quasiparticle band becomes fully polarized---an event marked by a sudden jump in the magnetic susceptibility. The system exhibits a kind of quantum rigidity in which the susceptibility (and several other physical observables) is insensitive to further increases in field strength. This behavior ends abruptly with the collapse of the hybridization order parameter in a first-order transition to the normal metallic state. We argue that the feature at ${B}^{*}$ corresponds to the ``metamagnetic transition'' in $\mathrm{Yb}{\mathrm{Rh}}_{2}{\mathrm{Si}}_{2}$. Our results are in good agreement with recent experimental measurements.

Dynamical mean field study of the two-dimensional disordered Hubbard model

We study the paramagnetic Anderson-Hubbard model using an extension of dynamical mean field theory (DMFT), known as statistical DMFT, that allows us to treat disorder and strong electronic correlations on equal footing. An approximate nonlocal Green's function is found for individual disorder realizations and then configuration averaged. We apply this method to two-dimensional lattices with up to 1000 sites in the strong disorder limit, where an atomic-limit approximation is made for the self-energy. We investigate the scaling of the inverse participation ratio at quarter- and half-filling, and find a nonmonotonic dependence of the localization length on the interaction strength. For strong disorder, we do not find evidence for an insulator-metal transition, and the disorder potential becomes unscreened near the Mott transition. Furthermore, strong correlations suppress the Altshuler-Aronov density of states anomaly near half-filling.