Mean-field Study Research Articles

Beyond relativistic mean-field studies of low-lying states in neutron-deficient krypton isotopes

Neutron-deficient krypton isotopes are of particular interest due to the coexistence of oblate and prolate shapes in low-lying states and the transition of ground-state from one dominate shape to another as a function of neutron number. A detailed interpretation of these phenomena in neutron-deficient Kr isotopes requires the use of a method going beyond a mean-field approach that permits to determine spectra and transition probabilities. The aim of this work is to provide a systematic calculation of low-lying state in the even-even 68-86Kr isotopes and to understand the shape coexistence phenomenon and the onset of large collectivity around N=40 from beyond relativistic mean-field studies. The starting point of our method is a set of relativistic mean-field+BCS wave functions generated with a constraint on triaxial deformations (beta, gamma). The excitation energies and electric multipole transition strengths of low-lying states are calculated by solving a five-dimensional collective Hamiltonian (5DCH) with parameters determined by the mean-field wave functions. To examine the role of triaxiality, a configuration mixing of both particle number (PN) and angular momentum (AM) projected axially deformed states is also carried out within the exact generator coordinate method (GCM) based on the same energy density functional. The energy surfaces, the excitation energies of 0^+_2, 2^+_1, 2^+_2 states, as well as the E0 and E2 transition strengths are compared with the results of similar 5DCH calculations but with parameters determined by the non-relativistic mean-field wave functions, as well as with the available data...

Non-Fermi-liquid behavior in cubic phase BaRuO3: A dynamical mean-field study

Motivated by the recently synthesized cubic phase BaRuO$_{3}$ under high pressure and high temperature, a thorough study has been conducted on its temperature-dependent electronic properties by using the state-of-the-art \textit{ab inito} computing framework of density functional theory combined with dynamical mean-field theory. At ambient condition the cubic phase BaRuO$_{3}$ should be a weakly correlated Hund's metal with local magnetic moment. The spin-spin correlation function and local magnetic susceptibility can be well described by the Curie-Weiss law over a wide temperature range. The calculated low-frequency self-energy functions of Ru-4d states apparently deviate from the behaviors predicted by Landau Fermi-liquid theory. Beyond that, the low-frequency optical conductivity can be fitted to a power-law $\Re\sigma(\omega) \sim \omega^{-0.98}$, which further confirms the Non-Fermi-liquid metallic state.

Field-induced Mott transition in kagome lattice Hubbard model

We investigate the magnetic-field effects on the Mott transition in the kagome lattice Hubbard model using the cellular dynamical mean-field theory combined with the continuous-time quantum Monte Carlo simulations. By calculating the magnetization and the momentum-resolved one-particle spectrum, we clarify that an applied magnetic field drives the first-order metal-insulator transition in a metallic phase around the zero-field Mott transition point. It is found that near the field-induced transition, the quasiparticle weight (effective mass) is increased (decreased) with increasing field, showing a sharp contrast to the results of the single-site dynamical mean-field study. The calculation of spin correlation functions elucidates that the nearest-neighbor antiferromagnetic correlations get enhanced with increasing field toward the transition point, indicating that the magnetic field stabilizes the insulating state with strong antiferromagnetic correlations.

RELATIVISTIC MEAN FIELD STUDY OF ISLANDS OF INVERSION IN NEUTRON-RICH Z = 17–23, 37–40 AND 60–64 NUCLEI

We study the extremely neutron-rich nuclei for Z = 17–23, 37–40 and 60–64 regions of the periodic table by using axially deformed relativistic mean field formalism with NL3* parametrization. Based on the analysis of binding energy, two neutron separation energy, quadrupole deformation and root mean square radii, we emphasized the speciality of these considered regions which are recently predicted islands of inversion.

Imaginary Polarization as a Way to Surmount the Sign Problem inAb InitioCalculations of Spin-Imbalanced Fermi Gases

From ultracold atoms to quantum chromodynamics, reliable abinitio studies of strongly interacting fermions require numerical methods, typically in some form of quantum MonteCarlo calculation. Unfortunately, (non)relativistic systems at finite density (spin polarization) generally have a sign problem, such that those abinitio calculations are impractical. It is well-known, however, that in the relativistic case imaginary chemical potentials solve this problem, assuming the data can be analytically continued to the real axis. Is this feasible for nonrelativistic systems? Are the interesting features of the phase diagram accessible in this manner? By introducing complex chemical potentials, for real total particle number and imaginary polarization, the sign problem is avoided in the nonrelativistic case. To give a first answer to the above questions, we perform a mean-field study of the finite-temperature phase diagram of spin-1/2 fermions with imaginary polarization.

Mobility edge phenomenon in a Hubbard chain: A mean field study

We show that a tight-binding one-dimensional chain composed of interacting and non-interacting atomic sites can exhibit multiple mobility edges at different values of carrier energy in presence of external electric field. Within a mean field Hartree-Fock approximation we numerically calculate two-terminal transport by using Green's function formalism. Several cases are analyzed depending on the arrangements of interacting and non-interacting atoms in the chain. The analysis may be helpful in designing mesoscale switching devices.

Antikaons and higher order couplings in the relativistic mean-field study of neutron stars

We investigate the role of higher order couplings, along with the condensation of antikaons (K− and ), on the properties of neutron stars (NS). We employ extended versions of the relativistic mean-field model, in which kaon–nucleon and nucleon–nucleon interactions are taken on the same footing. We find that the onset of condensation of K− and highly depends not only on the strength of optical potential but also on the new couplings. The presence of antikaons leads to a softer equation of state and makes the neutron star core symmetric and lepton-deficient. We show that these effects strongly influence the mass–radius relation as well as the composition of the neutron star. We also show that the recently observed 1.97±.04 solar mass NS can be explained in three ways: (i) a stiffer EoS with both antikaons, (ii) a relatively soft EoS with K− and (iii) a softer EoS without antikaons.

Monte Carlo Simulations and Theoretical Mean Field Analysis of Two Sites in the Oxidation of CO Over Cu0.1Ce0.9O2−y with Oxygen Supplied as the Gas and from the Catalyst’s Bulk

A kinetic Monte Carlo simulation algorithm and a theoretical mean field study of two sites is developed to interpret a redox mechanism based on that proposed by Sedmak et al. for the oxidation of CO over the nanostructured catalyst Cu0.1Ce0.9O2−y . The simulations reproduce adequately the published experimental results and the theoretical study allows the observation of some microscopic behaviour shown by this system. Simulation of the production $$ R_{{{\text{CO}}_{ 2} }} $$ at 200 °C as a function of origin of the oxygen. (filled square) Total $$ R_{{{\text{CO}}_{ 2} }} $$ , (filled circle) $$ R_{{{\text{CO}}_{ 2} }} $$ from the surface (opened circle) $$ R_{{{\text{CO}}_{ 2} }} $$ from the bulk of the catalyst.

Localised Wannier orbital basis for the Mott insulators GaV4S8 and GaTa4Se8

We study the electronic properties of GaV4S8 (GVS) and GaTa4Se8 (GTS), two distant members within the large family of chalcogenides AM4X8, with A = {Ga, Ge}, M = {V, Nb, Ta, Mo} and X = {S, Se}. While all these compounds are Mott insulators, their ground states show many types of magnetic order, with GVS being ferromagnetic and GTS non-magnetic. Based on their band structures, calculated with density functional theory methods, we compute an effective tight-binding Hamiltonian in a localised Wannier basis set, for each of the two compounds. The localised orbitals provide a very accurate representation of the band structure, with hopping amplitudes that rapidly decrease with distance. We estimate the superexchange interactions and show that the Coulomb repulsion with Hund's coupling may account the for the different ground states observed in GVS and GTS. Our localised Wannier basis provides a starting point for realistic dynamical mean-field theory studies of strong-correlation effects in this family compounds.

Spectral Properties of Correlated Materials: Local Vertex and Nonlocal Two-Particle Correlations from CombinedGWand Dynamical Mean Field Theory

We present a fully self-consistent combined GW and dynamical mean field (DMFT) study of the extended two-dimensional Hubbard model. The inclusion of the local dynamical vertex stemming from the DMFT self-energy and polarization is shown to cure the known problems of self-consistent GW. We calculate momentum-resolved spectral functions, two-particle polarizations, and electron-loss spectra, as well as the effective dynamical interaction induced by nonlocal screening. The momentum-dependence introduced by GW into the extended DMFT description leads to a narrowing of the quasiparticle width and more pronounced Hubbard bands in the metallic regime as one approaches the charge-ordering transition. It further affects the shape of collective modes, giving rise to dispersive plasmon-like long-wavelength and stripe modes.

Superfluidity of Dirac fermions in a tunable honeycomb lattice: Cooper pairing, collective modes, and critical currents

Motivated by recent experiments on atomic Dirac fermions in a tunable honeycomb optical lattice, we study the attractive Hubbard model of superfluidity in the anisotropic honeycomb lattice. At weak coupling, we find that the maximum mean-field pairing transition temperature, as a function of density and interaction strength, occurs for the case with isotropic hopping amplitudes. In this isotropic case, we go beyond mean-field theory and study collective fluctuations, treating both pairing and density fluctuations for interaction strengths ranging from weak to strong coupling. We find evidence for a sharp sound mode, together with a well-defined Leggett mode over a wide region of the phase diagram. We also calculate the superfluid order parameter and collective modes in the presence of nonzero superfluid flow. The flow-induced softening of these collective modes leads to dynamical instabilities involving stripelike density modulations as well as a Leggett-mode instability associated with the natural sublattice symmetry-breaking charge-ordered state on the honeycomb lattice. The latter provides a nontrivial test for the experimental realization of the one-band Hubbard model. We delineate regimes of the phase diagram where the critical current is limited by depairing or by such collective instabilities, and discuss experimental implications of our results.

Correlation Effects on 3D Topological Phases: From Bulk to Boundary

Topological phases of quantum matter defy characterization by conventional order parameters but can exhibit a quantized electromagnetic response and/or protected surface states. We examine such phenomena in a model for three-dimensional correlated complex oxides, the pyrochlore iridates. The model realizes interacting topological insulators, with and without time-reversal symmetry, and topological Weyl semimetals. We use cellular dynamical mean-field theory, a method that incorporates quantum many-body effects and allows us to evaluate the magnetoelectric topological response coefficient in correlated systems. This invariant is used to unravel the presence of an interacting axion insulator absent within a simple mean-field study. We corroborate our bulk results by studying the evolution of the topological boundary states in the presence of interactions. Consequences for experiments and for the search for correlated materials with symmetry-protected topological order are given.

Ground-state properties of the disordered spin-1 Bose-Hubbard model: A stochastic mean-field theory study

We study the ground state of the disordered Bose-Hubbard model for spin-1 particles by means of the stochastic mean-field theory. This approach enables the determination of the probability distributions of various physical quantities, such as the superfluid order parameter, the average site occupation number, the standard deviation of the occupation per site and the square of the spin operator per site. We show how a stochastic method, previously used in the study of localization, can be flexibly used to solve the relevant equations with great accuracy. We have determined the phase diagram, which exhibits three phases: the polar superfluid, the Mott insulating, and the Bose glass. A complete characterization of the physical properties of these phases has been established.

$\mathbb {Z}_2$ Z 2 -algebras in the Boolean function irreducible decomposition

We develop further the consequences of the irreducible-Boolean classification established by Zertuche, [“On the robustness of NK-Kauffman networks against changes in their connections and Boolean functions,” J. Math. Phys. 50, 043513 (2009)10.1063/1.3116166] which have the advantage of allowing strong statistical calculations in disordered Boolean function models, such as the NK-Kauffman networks. We construct a ring-isomorphism \documentclass[12pt]{minimal}\begin{document}$\mathfrak {R}_K \left\lbrace i_1, \dots , i_\lambda \right\rbrace \cong \mathcal {P}^2 \left[ K \right]$\end{document}RKi1,⋯,iλ≅P2K of the set of reducible K-Boolean functions that are reducible in the Boolean arguments with indexes {i1, …, iλ}, and the double power set \documentclass[12pt]{minimal}\begin{document}$\mathcal {P}^2 \left[ K \right]$\end{document}P2K of the first K natural numbers. This allows us, among other things, to calculate the number ϱK(λ, ω) of K-Boolean functions which are λ-irreducible with weight ω. ϱK(λ, ω) is a fundamental quantity in the study of the stability of NK-Kauffman networks against changes in their connections between their Boolean functions, as well as in the mean field study of their dynamics when Boolean irreducibility is taken into account.

Band Jahn–Teller effect on the density of states of the magnetic high-Tc superconductors: A model study

We report here a mean-field study of competing antiferromagnetism, superconductivity and lattice strain phases and their effect on the local density of states of the cuprate system. Our model Hamiltonian incorporating these interactions is reported earlier [G.C. Rout et al., Physica C, 2007]. The analytic expression for superconducting, antiferromagnetism and lattice strain order parameters are calculated and solved self-consistently. The interplay of these order parameters is investigated considering the calculated density of states (DOSs) of the conduction electrons. The DOS displays multiple gap structures with multiple peaks. It is suggested that the tunneling conductance data obtained from the scanning tunneling microscopy (STM) measurements could be interpreted by using the quasi-particle bands calculated from our model Hamiltonian. We have discussed the mechanism to calculate the order parameters from the conductance data.

Hydrophobic droplets in amphiphilic bilayers: a coarse-grained mean-field theory study

Hydrophobic molecules such as oils and certain drugs can be encapsulated between the two leaflets of an amphiphilic bilayer in both lipid and polymer systems. We investigate the case where the hydrophobic molecules are incompatible with the amphiphile tails and so form droplets. Using a coarse-grained mean-field model (self-consistent field theory, or SCFT), we find that droplets of a wide range of sizes have the same characteristic lens shape, and explain this result in terms of simple capillarity arguments, consistent with the measured variations of surface concentrations of amphiphile in the bilayer and in the monolayers that cover the droplet. We study the effect of the strength chi_BO of the repulsion between the hydrophobic liquid and the amphiphile tails on the droplet shape, and find a gradual flattening of the droplet as chi_BO is reduced. The droplet remains at least metastable even at very low values of chi_BO. This is in contrast to the behavior as the length of the hydrophobic molecules is varied. Specifically, if these molecules are at least as long as the amphiphile tails, increasing their length further is found to have little effect on the droplet shape, while reducing their length below this value quickly causes the droplet to become unstable.

Spontaneous formation of permanent shear bands in a mesoscopic model of flowing disordered matter

This study proposes a coherent scenario of the formation of permanent shear bands in the flow of yield stress materials. It is a well accepted point of view that flow in disordered media occurs via local plastic events, corresponding to small size rearrangements, that yield a long range stress redistribution over the system. Within a minimalistic mesoscopic model that incorporates these local dynamics, we study the spatial organisation of the local plastic events. The most important parameter in this study is the typical restructuring time needed to regain the original structure after a local rearrangement. In agreement with a recent mean field study [Coussot et al., Eur. Phys. J. E, 2010, 33, 183] we observed the spontaneous formation of permanent shear bands, when this restructuring time is large compared to the typical stress release time in a rearrangement. The bands consist of a large number of plastic events within a solid region that remains elastic. This heterogeneous flow behaviour is different in nature from the transient dynamical heterogeneities that one observes in the small shear rate limit in flow without shear-banding [Martens et al., Phys. Rev. Lett., 2011, 106, 156001]. We analyse in detail the dependence of the shear bands on system size, shear rate and restructuring time. Further, we rationalise the scenario within a mean field version of the spatial model that produces a non monotonous flow curve for large restructuring times. This explains the instability of the homogeneous flow below a critical shear rate, that corresponds to the minimum of the curve. Our study therefore strongly supports the idea that the characteristic time scales involved in the local dynamics are at the physical origin of permanent shear bands.

Doping the Kane-Mele-Hubbard model: A slave-boson approach

We study the Kane-Mele-Hubbard model both at half-filling and away from half-filling using a slave-boson mean-field approach at zero temperature. We obtain a phase diagram at half-filling and discuss its connection to recent results from quantum Monte Carlo, cellular dynamical mean field, slave-rotor, and ${Z}_{2}$ mean-field studies. In particular, we find a small window in parameter space where a spin-liquid phase with gapped spin and charge excitations reside. Upon doping, we show the spin-liquid state becomes a superconducting state by explicitly calculating the singlet pairing order parameters. Interestingly, we find an ``optimal'' doping for such superconductivity. Our work reveals some of the phenomenology associated with doping an interacting system with strong spin-orbit coupling and intermediate strength electron-electron interactions.

Zero- and finite-temperature mean field study of magnetic field induced electric polarization in Ba2CoGe2O7: Effect of the antiferroelectric coupling

We investigate the spin induced polarization in the multiferroic compound Ba${}_{2}$CoGe${}_{2}$O${}_{7}$ using variational and finite-temperature mean field approaches, with the aim to reproduce the peculiar behavior of the induced polarization in a magnetic field observed experimentally in Murakawa et al. [Phys. Rev. Lett. 105, 137202 (2010)]. The compound is usually described by a spin-3/2 Heisenberg model extended with easy-plane anisotropy and Dzyaloshinskii-Moriya (DM) interaction. By applying a magnetic field parallel to the $[110]$ axis, three phases can be distinguished in this model: (i) At high magnetic field, we find a partially magnetized phase with spins parallel to the fields and uniform polarization. (ii) Below a critical field, the ground state is a twofold-degenerate canted antiferromagnet, where the degeneracy can be lifted by a finite DM interaction. (iii) At zero field, a U$(1)$ symmetry-breaking phase takes place, exhibiting a Goldstone mode. We find that extending the Hamiltonian with an antiferroelectric term results in the appearance of a canted ferrimagnetic phase for $h\ensuremath{\lesssim}1$ T. This phase is characterized by a finite staggered polarization, as well as by a magnetization closing a finite angle with the applied field leading to torque anomalies.

Dynamical Mean Field Study of the Kondo Lattice Model with Frustration

We analyze the antiferromagnetic Kondo lattice model for the two-dimensional square lattice including frustration. The Kondo lattice model is especially interesting in the context of heavy fermion physics, as it possibly exhibits a quantum phase transition between an antiferromagnetically ordered state and a paramagnetic heavy Fermion state. The latter can, depending on the electronic properties be either a metallic state with dynamically generated flat bands at the Fermi energy, or an insulator, the so-called Kondo insulator. We analyze the effects of next nearest neighbor (NNN) hopping upon the properties of the Kondo lattice model, especially focusing on the paramagnetic and antiferromagnetic properties around half filling. To this end we use the dynamical mean field theory (DMFT) with the Numerical Renormalization Group (NRG) as an impurity solver. Whereas the paramagnetic results remain qualitatively unchanged when introducing the NNN hopping, the Néel state at half filling is replaced by a spin-density wave. Also the transition between the magnetic ordered state and the Kondo insulator depends on the NNN hopping. An interesting effect of the NNN hopping is the stabilization of Néel states away from half filling.