Variational Scheme for the Mott Transition

The Hubbard model is studied at half filling, using two complementary variational wave functions, the Gutzwiller ansatz for the metallic phase at small values of the interaction parameter U and its analog for the insulating phase at large values of U. The metallic phase is characterized by the Drude weight, which exhibits a jump at the critical point U_c. In the insulating phase the system behaves as a collection of dipoles which increase both in number and in size as U gets smaller. The two wave functions are able to describe the two asymptotic regimes (small and large values of U, respectively), but they can no longer be trusted in the region of the Mott transition (UU_c). More powerful methods are needed to study, for instance, the divergence of the electric susceptibility for UU_c.     

Quantum phase transition of cold atoms trapped in optical lattices

We review our recent theoretical advances in phase transition of cold atoms in optical lattices, such as triangular lattice, honeycomb lattice, and Kagomé lattice. By employing the new developed numerical methods called dynamical cluster approximation and cellular dynamical mean-field theory, the properties in different phases of cold atoms in optical lattices are studied, such as density of states, Fermi surface and double occupancy. On triangular lattice, a reentrant behavior of phase translation line between Fermi liquid state and pseudogap state is found due to the Kondo effect. We find the system undergoes a second order Mott transition from a metallic state into a Mott insulator state on honeycomb lattice and triangular Kagomé lattice. The stability of quantum spin Hall phase towards interaction on honeycomb lattice with spin-orbital coupling is systematically discussed. And we investigate the transition from quantum spin Hall insulator to normal insulator in Kagomé lattice which includes a nearest-neighbor intrinsic spin-orbit coupling and a trimerized Hamiltonian. In addition, we propose the experimental protocols to observe these phase transition of cold atoms in optical lattices.     

Time-dependent Mott transition in the periodic Anderson model with nonlocal hybridization

The time-dependent Mott transition in a periodic Anderson model with off-site,nearest-neighbor hybridization is studied within the framework of nonequilibriumself-energy functional theory. Using the two-site dynamical-impurity approximation, wecompute the real-time dynamics of the optimal variational parameter and of differentobservables initiated by sudden quenches of the Hubbard-U and identify the criticalinteraction. The time-dependent transition is orbital selective, i.e., in the final state,reached in the long-time limit after the quench to the critical interaction, the Mott gapopens in the spectral function of the localized orbitals only. We discuss the dependenceof the critical interaction and of the final-state effective temperature on thehybridization strength and point out the various similarities between the nonequilibriumand the equilibrium Mott transition. It is shown that these can also be smoothly connectedto each other by increasing the duration of a U-ramp from a sudden quench to a quasi-staticprocess. The physics found for the model with off-site hybridization is compared with thedynamical Mott transition in the single-orbital Hubbard model and with the dynamicalcrossover found for the real-time dynamics of the conventional Anderson lattice withon-site hybridization.     

Doublon–holon-binding mechanism of Mott transition in 2D Hubbard model

The mechanism of nonmagnetic Mott transitions in the Hubbard model on the square lattice is studied, using a variational Monte Carlo method. A simple doublon (D)–holon (H) binding mechanism a previous study proposed [J. Phys. Soc. Jpn. 75 (2006) 114706] has to be modified, because even a wave function with completely bound D–H pairs brings about a Mott transition at a finite correlation strength. By introducing two characteristic lengths, D–H pair binding length, ξ_DH, and minimum inter-doublon distance, ξ_DD, we can properly describe the physics of Mott transitions, and determine the critical point by ξ_DD ～ ξ_DH. This concept seems universal, because it is valid not only for newly introduced wave functions with long-range D–H and D–D (H–H) correlation factors discussed here, but for a wide range of wave functions with D–H binding factors.     

Ferromagnetism in the Hubbard model: instability of the Nagaoka state on the triangular,honeycomb and kagome lattices

In order to analyse the lattice dependence of ferromagnetism in the two-dimensional Hubbard model we investigate the instability of the fully polarised ferromagnetic ground state (Nagaoka state) on the triangular, honeycomb and kagome lattices. We mainly focus on the local instability, applying single spin flip variational wave functions which include majority spin correlation effects. The question of global instability and phase separation is addressed in the framework of Hartree-Fock theory. We find a strong tendency towards Nagaoka ferromagnetism on the non-bipartite lattices (triangular, kagome) for more than half filling. For the triangular lattice we find the Nagaoka state to be unstable above a critical density of n = 1.887 at U = ∞, thereby significantly improving former variational results. For the kagome lattice the region where ferromagnetism prevails in the phase diagram widely exceeds the flat band regime. Our results even allow the stability of the Nagaoka state in a small region below half filling. In the case of the bipartite honeycomb lattice several disconnected regions are left for a possible Nagaoka ground state.     

The simplified Hubbard model in one and two dimensions

Thermodynamic and dynamic properties of the one and two-dimensional simplified Hubbard model are studied. At zero temperature and half filling, no metal-insulator transition occurs for nonzero couplingU and the system is an antiferromagnetic insulator. The behavior of the gap in the single-particle density of states is investigated as a function ofU, temperature and band fillingp. For weak to intermediate coupling the gap at half filling closes for increasing temperatures. The ground state of doped lattices exhibits a metal-insulator transition at ?4d<U _c (p)≦?2d (d is the lattice dimensionality) and displays ferromagnetism without long-range order forU>U _c . The co-existence for variable temperatures and electron densities of metallic behavior and magnetic and charge-density long-range order is demonstrated. The critical temperature for long-range order is calculated for the half-filled two-dimensional case. Results for the optical conductivity and several thermodynamic properties are presented.     

Gauge field thermodynamics for the SU(2) Yang-Mills system

After reviewing the euclidean formulation of the thermodynamics for quantum spin systems, we develop the corresponding formalism for SU(N) gauge fields on the lattice. The results are then evaluated for the SU(2) system, using Monte Carlo simulation on lattices of (space × temperature) size 10³ × 2,3,4,5. At high temperature, the system exhibits Stefan-Boltzmann behaviour, with three gluonic colour degrees of freedom. At T_c ≈ 43Λ_L (215 MeV), the transition to “hadronic” behaviour occurs, signalled by a sharp peak in the specific heat. From the behaviour below the deconfinement transition (T<T_c), we obtain m_G ≈ 200Λ_L (1000 MeV) for the mass of the lowest gluonium state (glueball).     

Inelastic neutron scattering study of commensurate-incommensurate phase transition in thiourea

This paper presents a study of the nature of the incommensurate lattice instability in deuterated thiourea by inelastic neutron scattering. It shows clearly a “soft mode” which condenses at the phase transition in a satellite reflexion. A study of related dispersion curves along the [O ξ O] direction shows an unusual spectral shape in a large temperature range above T_c.     

Frustration of antiferromagnetism in the t-t′-Hubbard model at weak coupling

The perfect-nesting instability towards antiferromagnetism of the Hubbard model is suppressed by next-nearest neighbor hopping t′. The asymptotic behavior of the critical coupling U_c(t′) at small t′ is calculated in dimensions d = 2,3, ∞ using Hartree theory; this yields the exact result at least in d > 2. The order of the transition is also determined. A region of stability of a metallic antiferromagnetic phase in d = 3 is identified.     

Critical behaviour near the metal-insulator transition of a doped Mott insulator

We have studied the critical behaviour of a doped Mott insulator near the metal-insulator transition for the infinite-dimensional Hubbard model using a linearized form of dynamical mean-field theory. The discontinuity in the chemical potential in the change from hole to electron doping, for U larger than a critical value U _c, has been calculated analytically and is found to be in good agreement with the results of numerical methods. We have also derived analytic expressions for the compressibility, the quasiparticle weight, the double occupancy and the local spin susceptibility near half-filling as functions of the on-site Coulomb interaction and the doping. Received 15 March 2001 and Received in final form 22 May 2001     

Equilibrium properties of fast-rotating headed nuclei

We report on calculations of the equilibrium deformation in excited heated rotating nuclei. At A ～ 150–200 and temperature t > t_c ≈ 1.2 MeV the shell effects turn out to be small to compete with the variations of the liquid drop component of the energy. The transition from the shape of a “cool” nucleus to that of a “hot” nucleus takes place at t_c and in deformed nuclei resembles a phase transition. The stiffness parameter with respect to shape variations at t_c is anomalously low.     

System-parameter dependence of the metallic phase of the non-doped 2D Hubbard model

Naito et al. reported that some non-doped T′-214-type compounds drive high-T_c superconductivity. The compounds are considered to be metallic since on-site Coulomb energy U is moderate and the Fermi surface is much deformed in these compounds. In order to confirm this picture and extract electronic structure information, we have examined the phase diagram of the metallic state of the 2D Hubbard model as a function of U and t′ (with t″ we fixed at − t′/2 here; t′ and t″ are the second- and third-neighbor transfer energies, respectively) by means of the variational Monte–Carlo method. We employed a Jastrow-type Gutzwiller trial wave function. In the studied range of U = 2–12, the boundary value for |t′| at which SDW disappears increases almost linearly with U. Jump-wise transition to the Mott insulator state was not observed. Using the boundary curve and experimental band parameter values, we estimate U  5 for T′-214 compounds. Preceding works are discussed in the last part.     

Flow equations for the ionic Hubbard model

Taking the site-diagonal terms of the ionic Hubbard model (IHM) in one and two spatial dimensions, as H₀, we employ Continuous Unitary Transformations (CUT) to obtain a “classical” effective Hamiltonian in which hopping term has been renormalized to zero. For this Hamiltonian spin gap and charge gap are calculated at half-filling and subject to periodic boundary conditions. Our calculations indicate two transition points. In fixed Δ, as U increases from zero, there is a region in which both spin gap and charge gap are positive and identical; characteristic of band insulators. Upon further increasing U, first transition occurs at U=Uc₁, where spin and charge gaps both vanish and remain zero up to U=Uc₂. A gap-less state in charge and spin sectors characterizes a metal. For U>Uc₂ spin gap remains zero and charge gap becomes positive. This third region corresponds to a Mott insulator in which charge excitations are gaped, while spin excitations remain gap-less.     

Ferromagnetism in the Hubbard model: instability of the Nagaoka state on the square lattice

The instability of the fully polarized ferromagnetic ground state (Nagaoka state) of the Hubbard model on the square lattice is investigated. We use single spin flip variational wave functions including majority spin correlation effects and calculate spin flip energies in the thermodynamic limit. With very local wave functions and with moderate numbers of variational parameters we reproduce the best known estimate for the critical hole density δ_cr = 0.29 and we obtain an estimate of U_cr = 63 t for the critical coupling which is considerably better than the best estimate of U_cr = 42 t previously known. The simplicity of our wave functions makes the physical origin of the various aspects of the instability particularly transparent.     

A stability analysis of fifth-order water wave models

We study the stability of traveling wave solutions to a fifth-order water wave model. By solving a constrained minimization problem we show that “ground state” traveling wave solutions exist. Their stability is shown to be determined by the convexity or concavity of a function d(c) of the wave speed c. The analysis makes frequent use of the variational properties of the traveling waves.     

Soft plasmon theory of the new high-temperature superconductors

The newly-discovered high-temperature superconductors are close to, but on the metallic side of, a Mott metal — insulator transition. The incipient Mott transition manifests itself as a tendency towards a charge density wave instability, characterized by wave vectors appropriate for Fermi-surface nesting. In La₂CuO₄, this charge-density wave is commensurate with the lattice, and leads to a structural transition to a non-metallic state. We show that in the new superconducting materials, this incipient instability causes a drastic softening of the plasmon modes at these wave vectors. Indeed, there is some experimental evidence for such soft plasmons in these materials. Although these modes have a much lower frequency than ordinary plasmons, it is still much higher than the Debye-cut-off phonon frequency. They are strongly coupled to the conduction electrons, and induce an electron - electron attraction in a way analogous to phonons. Moreover, the soft-plasmon wave vectors are automatically those required for Cooper pairing, since they connect points on the Fermi surface. The Debye-energy prefactor in the BCS expression for the transition temperature is replaced by the considerably larger plasmon energy. Furthermore the strength of the interaction will ensure that the exponential factor is not too small. Note that this mechanism will lead to zero isotope effect. We suggest that the Ba or La f-orbitals play an important role in softening these plasma modes and strengthening the electron - plasmon coupling. This would explain why the presence of Ba or La seems to be favourable for high-temperature superconductivity.     

Ferromagnetism in the Hubbard model on the square lattice: Improved instability criterion for the Nagaoka state

The instability of the fully polarized ferromagnetic state (Nagaoka state) with respect to single spin flips is re-examined for the Hubbard model on the square lattice with a large family of variational wave functions which include correlation effects of the majority spins in the vicinity of the flipped spin. We find a critical hole density of δ_cr = 0.251 for U = ∞ and a critical coupling of U_cr = 77.7t. Both values improve previous variational results considerably.     

Mechanism of superfluid-insulator transition in two-dimensional Bose Hubbard model

To understand the mechanism of Mott transitions in case of no magnetic influence, superfluid-insulator (Mott) transitions are studied for the S = 0 Bose Hubbard model on the square lattice, using a variational Monte Carlo approach. In trial many-body wave functions, we introduce various types of attractive correlation factors between a doubly-occupied site (doublon, D) and an empty site (holon, H), which play a central role for the transition. We propose an improved picture of D–H binding; a Mott transition occurs when the D–H pair length becomes equivalent to the minimum D–D distance, which lengths are appropriately estimated. We confirm this picture is valid for all the wave functions with attractive D–H factors we consider, and point out it can be universal for nonmagnetic Mott transitions.     

Competition between crystalline electric field singlet and itinerant states of f electrons

A new kind of phase transition is proposed for lattice fermion systems with simplified f ² configurations at each site. The free energy of the model is computed in the mean-field approximation for both the itinerant state with the Kondo screening, and a localized state with the crystalline electric field (CEF) singlet at each site. The presence of a first-order phase transition is demonstrated in which the itinerant state changes into the localized state toward lower temperatures. In the half-filled case, the insulating state at high temperatures changes into a metallic state, in marked contrast with the Mott transition in the Hubbard model. For comparison, corresponding states are discussed for the twoimpurity Kondo system with f ¹ configuration at each site.     

Superconductivity in a simple model of the pseudogap state

An analysis is made of characteristics of the superconducting state (s-and d-pairing) using a simple, exactly solvable model of the pseudogap state produced by fluctuations of the short-range order (such as antiferromagnetic) based on a Fermi surface model with “hot” sections. It is shown that the superconducting gap averaged over these fluctuations is nonzero at temperatures higher than the mean-field superconducting transition temperature T _c over the entire sample. At temperatures T > T _c superconductivity evidently exists in isolated sections (“ drops”). Studies are made of the spectral density and the density of states in which superconducting characteristics exist in the range T > T _c however, in this sense the temperature T = T _c itself is no different in any way. These anomalies show qualitative agreement with various experiments using underdoped high-temperature superconducting cuprates.