Mott transition in kagomé lattice Hubbard model

We investigate the Mott transition in the kagomé lattice Hubbard model using a cluster extension of dynamical mean field theory. The calculation of the double occupancy, the density of states, and the static and dynamical spin correlation functions demonstrates that the system undergoes the first-order Mott transition at the Hubbard interaction U/W approximately 1.4 (W:bandwidth). In the metallic phase close to the Mott transition, we find the strong renormalization of three distinct bands, giving rise to the formation of heavy quasiparticles with strong frustrated interactions. It is elucidated that the quasiparticle states exhibit anomalous behavior in the temperature-dependent spin correlation functions.     

Quantum coherence and ground-state phase transition in a four-chain Bose–Hubbard model

We study the quantum coherence and ground-state phase transition of a four-chain Bose–Hubbard model with the long-range interaction. In a special four-chain Bose–Hubbard model,i.e., each chain only has one optical potential, four types of the ground-state phases are discovered. The effects of the disorder, the on-site interaction and the long-range interaction on the quantum coherence are studied. For the system without the long-range interaction, the quantum coherence changes from one periodic oscillation to two periodic oscillations as the onsite interaction increases. By considering the long-range interaction, the quantum coherence goes back to one periodic oscillation again. The on-site interaction itself suppresses the quantum coherence, both the on-site interaction and long-range interaction together enhance the quantum coherence with the weak disorder. If the disorder strength is increased beyond a critical value,they start to suppress the quantum coherence. In a regular four-chain Bose–Hubbard model, i.e.,each chain has many optical potentials, the ground-state phase transitions are obtained by using the cluster Gutzwiller mean-field method. Exotic ground-state phases are found, i.e., superfluid phase, integer Mott insulator phase, supersolid phase and loophole insulator phase. The combination of the loophole insulator phase and the supersolid phase expands the lobes with the half-integer filling per site for the small ratio β = t_■/t_⊥.     

Spin crossovers in Mott–Hubbard insulators at high pressures

The high-pressure induced phase transitions initiated by electronic transition in 3d ions from the high-spin (HS) to the low-spin (LS) state (HS-LS spin-crossover) are considered. Behavior of the system with d⁶ electronic configuration is investigated in the ground state of zero temperature and critical pressure P_c. Magnetic properties of the Mott–Hubbard insulator (Mg_1−xFe_x)O are studied in the vicinity of the quantum critical point (T=0, P_c). At the critical pressure of spin crossover P_c, the spin gap energy ε_S between HS and LS states is zero. The quantum spins fluctuations HS⇔LS do not require any energy, and the antiferromagnetism is destroyed in the quantum critical point by the first order transition.     

Study of supersolidity in the two-dimensional Hubbard–Holstein model

We derive an effective Hamiltonian for the two-dimensional Hubbard–Holstein model in the regimes of strong electron–electron and strong electron–phonon interactions by using a nonperturbative approach. In the parameter region where the system manifests the existence of a correlated singlet phase, the effective Hamiltonian transforms to a t₁ ? V ₁ ? V ₂ ? V ₃ Hamiltonian for hard-core-bosons on a checkerboard lattice. We employ quantum Monte Carlo simulations, involving stochastic-series-expansion technique, to obtain the ground state phase diagram. At filling 1∕8, as the strength of off-site repulsion increases, the system undergoes a first-order transition from a superfluid to a diagonal striped solid with ordering wavevector \(\vec{Q}\) = (π∕4, 3π∕4) or (π∕4, 5π∕4). Unlike the one-dimensional situation, our results in the two-dimensional case reveal a supersolid phase (corresponding to the diagonal striped solid) around filling 1∕8 and at large off-site repulsions. Furthermore, for small off-site repulsions, we witness a valence bond solid at one-fourth filling and tiny phase-separated regions at slightly higher fillings.     

Thermodynamics of the 3D Hubbard model on approaching the Néel transition

We study the thermodynamic properties of the 3D Hubbard model for temperatures down to the Néel temperature by using cluster dynamical mean-field theory. In particular, we calculate the energy, entropy, density, double occupancy, and nearest-neighbor spin correlations as a function of chemical potential, temperature, and repulsion strength. To make contact with cold-gas experiments, we also compute properties of the system subject to an external trap in the local density approximation. We find that an entropy per particle S/N ≈ 0.65(6) at U/t = 8 is sufficient to achieve a Néel state in the center of the trap, substantially higher than the entropy required in a homogeneous system. Precursors to antiferromagnetism can clearly be observed in nearest-neighbor spin correlators.     

Temperature effects on superfluid phase transition in Bose–Hubbard model with three-body interaction

We theoretically investigate the effect of the three-body on-site interactions on the Mott-insulator–superfluid transition for ultracold bosonic atoms in the framework of the Bose–Hubbard model. In particular, we explore the combined effects of three-body interaction and finite temperature on the phase diagram in detail. In order to handle system with strong local interactions a resolvent expansion technique based on the contour integral representation of the partition function has been devised. Subsequently, we derive the Landau-type expansion for the free energy in terms of the superfluid order parameter and find the phase diagrams depicting the relationships between various physical quantities of interest.     

Benchmark study of the SF-MI phase transition of the Bose–Hubbard model with density-induced tunneling

The Bose–Hubbard model (BHM) is a standard model which describes the quantum behavior of ultracold bosons in optical lattice. When tuning the model parameters, a quantum phase transition from superfluid (SF) phase to Mott insulating (MI) phase emerges. However, an extra tunneling process – the density-induced tunneling – is usually ignored in the standard BHM. Using process-chain method, we give a thorough study of the phase diagram of the BHM with density-induced tunneling in different particle density regions and spatial dimensions. We find the density-induced tunneling process can affect the SF-MI phase boundary dramatically, by suppressing the MI region and tune the tip of the phase boundary to lower chemical potential. Our unbiased numerical study gives benchmark results of the phase diagram of the BHM with density-induced tunneling.     

Excitonic metal–insulator phase transition of the Mott type in compressed calcium

It has been experimentally found that, under the static compression of a calcium crystal at room temperature, it undergoes a series of structural phase transitions: face-centered cubic lattice → body-centered cubic lattice → simple cubic lattice. It has been decided to investigate precisely the simple cubic lattice (because it is an alternative lattice) with the aim of elucidating the possibility of the existence of other (nonstructural) phase transitions in it by using for this purpose the Hubbard model for electrons with half-filled ns-bands and preliminarily transforming the initial electronic system into an electron–hole system by means of the known Shiba operators (applicable only to alternative lattices). This transformation leads to the fact that, in the new system of fermions, instead of the former repulsion, there is an attraction between electrons and holes. Elementary excitations of this new system are bound boson pairs—excitons. This system of fermions has been quantitatively analyzed by jointly using the equation-of-motion method and the direct algebraic method. The numerical integration of the analytically exact transcendental equations derived from the first principles for alternative (one-, two-, and three-dimensional) lattices has demonstrated that, in systems of two-species (electrons + hole) fermions, temperature-induced metal–insulator phase transitions of the Mott type are actually possible. Moreover, all these crystals are in fact excitonic insulators. This conclusion is in complete agreement with the analytically exact calculations of the ground state of a one-dimensional crystal (with half-filled bands), which were performed by Lieb and Wu with the aim to find out the Mott insulator–metal transition of another type.     

Ginzburg–Landau expansion in strongly disordered attractive Anderson–Hubbard model

We have studied disordering effects on the coefficients of Ginzburg–Landau expansion in powers of superconducting order parameter in the attractive Anderson–Hubbard model within the generalized DMFT+Σ approximation. We consider the wide region of attractive potentials U from the weak coupling region, where superconductivity is described by BCS model, to the strong coupling region, where the superconducting transition is related with Bose–Einstein condensation (ВЕС) of compact Cooper pairs formed at temperatures essentially larger than the temperature of superconducting transition, and a wide range of disorder—from weak to strong, where the system is in the vicinity of Anderson transition. In the case of semielliptic bare density of states, disorder’s influence upon the coefficients A and В of the square and the fourth power of the order parameter is universal for any value of electron correlation and is related only to the general disorder widening of the bare band (generalized Anderson theorem). Such universality is absent for the gradient term expansion coefficient C. In the usual theory of “dirty” superconductors, the С coefficient drops with the growth of disorder. In the limit of strong disorder in BCS limit, the coefficient С is very sensitive to the effects of Anderson localization, which lead to its further drop with disorder growth up to the region of the Anderson insulator. In the region of BCS–ВЕС crossover and in ВЕС limit, the coefficient С and all related physical properties are weakly dependent on disorder. In particular, this leads to relatively weak disorder dependence of both penetration depth and coherence lengths, as well as of related slope of the upper critical magnetic field at superconducting transition, in the region of very strong coupling.     

Hund’s coupling and the metal-insulator transition in the two-band Hubbard model

The Mott-Hubbard metal-insulator transition is investigated in a two-band Hubbard model within dynamical mean-field theory. To this end, we use a suitable extension of Wilsons numerical renormalization group for the solution of the effective two-band single-impurity Anderson model. This method is non-perturbative and, in particular, allows to take into account the full exchange part of the Hunds rule coupling between the two orbitals. We discuss in detail the influence of the various Coulomb interactions on thermodynamic and dynamic properties, for both the impurity and the lattice model. The exchange part of the Hunds rule coupling turns out to play an important role for the physics of the two-band Hubbard model and for the nature of the Mott-transition.     

On the nature of the phase transition triggered by vortex-like defects in the 2D Ginzburg–Landau model

The two-dimensional lattice Ginzburg–Landau Hamiltonian is simulated numerically for different values of the coherence length ξ in units of the lattice spacing a, a parameter which controls amplitude fluctuations. The phase diagram on the plane T–ξ is measured. Amplitude fluctuations change dramatically the nature of the phase transition: for values of ξ/a≃1, instead of the smooth Kosterlitz–Thouless transition there is a first-order transition with a discontinuity in the vortex density v and a sharper drop in the helicity modulus Γ. Both observables v and Γ are analyzed in detail at the crossover region between first and second order which occurs for intermediate values of ξ/a.     

Absence of pair binding in the U=∞ Hubbard model

We consider the standard Hubbard model in the U= limit. We show that, for any finite lattice with all positive hopping matrix elements, t _i,j >0, the ground state energy of the system containing two particles in excess of half filling plus the energy of the system at half filling is never lower than twice the energy of the system with a single extra particle. Similar results are obtained for holes when the lattice is bipartite. As a byproduct, we obtain a simple alternative proof of Tasaki's generalization of the Nagaoka theorem for non-bipartite lattices (but without the uniqueness clause).     

Perturbative calculation of critical exponents for the Bose–Hubbard model

We develop a strategy for calculating critical exponents for the Mott insulator-to-superfluid transition shown by the Bose–Hubbard model. Our approach is based on the field-theoretic concept of the effective potential, which provides a natural extension of the Landau theory of phase transitions to quantum critical phenomena. The coefficients of the Landau expansion of that effective potential are obtained by high-order perturbation theory. We counteract the divergency of the weak-coupling perturbation series by including the seldom considered Landau coefficient a ₆ into our analysis. Our preliminary results indicate that the critical exponents for both the condensate density and the superfluid density, as derived from the two-dimensional Bose–Hubbard model, deviate by less than 1 % from the best known estimates computed so far for the three-dimensional XY universality class.     

Ground-state phase diagram of the 1-D Holstein–Hubbard model

The Holstein–Hubbard model is investigated in one-dimension at half filling employing a series of unitary transformations taking into account the coherence and correlation of phonons. To treat the phonon subsystem more accurately a new squeezing transformation is introduced to incorporate the electron-density-dependent onsite phonon correlations to lower the energy further. The effective electronic Hamiltonian is next obtained by averaging the transformed Hamiltonian with respect to the zero-phonon state and the resulting effective electronic Hamiltonian is solved exactly using the method of Bethe ansatz. Finally the ground state is obtained by minimizing the energy with respect to all the variational parameters. The present method gives better results for the ground state energy of the system and also suggests the existence of a wider intermediate metallic phase at the charge-density-wave–spin-density-wave crossover region, which was first predicted by Takada and Chatterjee and later supported by Krishna and Chatterjee.     

Universality of the Mott–Ioffe–Regel limit in metals

The absence of resistivity saturation in many strongly correlated metals, including the high-temperature superconductors, is critically examined from the viewpoint of optical conductivity measurements. Coherent quasiparticle conductivity, in the form of a Drude peak centred at zero frequency, is found to disappear as the mean free path (at ω?=?0) becomes comparable with the interatomic spacing. This basic loss of coherence at the so-called Mott–Ioffe–Regel (MIR) limit suggests that the universality of the MIR criterion is preserved even in the presence of strong electron correlations. We argue that the shedding of spectral weight at low frequencies, induced by strong correlation effects, is the primary origin of the extended positive slope of the resistivity to high temperatures observed in all so-called ‘bad metals’. Moreover, in common with those metals which exhibit resistivity saturation at high temperatures, the scattering rate itself, as extracted from optical spectra, saturates at a value consistent with the MIR limit. We consider possible implications that this ceiling in the scattering rate may have for our understanding of transport within a wide variety of bad metals and suggest a better method for analysing their optical response.     

Solidification mechanism transition of liquid Co–Cu–Ni ternary alloy

We report a solidification mechanism transition of liquid ternary Co₄₅Cu₄₅Ni₁₀ alloy when it solidifies at a critical undercooling of about 344 K. When undercooling at ΔT<344 K, the solidification process is characterized by primary S (Co) dendritic growth and a subsequent peritectic transition. The dendritic growth velocity of S (Co) dendrite increases with the rise of undercooling. However, once ΔT>344 K, the solidification velocity decreases with the increase of undercooling. In this case, liquid/liquid phase separation takes place prior to solidification. The minor L₂ (Cu) droplets hinder the motion of the solidification front, and a monotectic transition may occur in the major L₁ phase. These facts caused by metastable phase separation are responsible for the slow growth at high undercoolings.     

Inherent mechanism of breakdown in laminar-turbulent transition of plane channel flows

We will first list some known facts of transition and turbulence, and then analyze results from direct numerical simulations done for the transition of plane channel flows, thus revealing the key mechanism of breakdown. 1 Arguments based on known facts A superficial reason for the fact that the change of mean flow profile plays the key role in transition is that the mean flow profiles for laminar and turbulent flow are drasti- cally different. But this does not provide the inherent mechanism o…