Quantum Entanglement in Ground State of Extended Hubbard Model

Metal-insulator and CDW-SDW transitions are studied in the one-dimensional Extended Hubbard Model at half-filling by analysing the behaviour of local entanglement in fermionic systems. 1D traditional Hubbard model exhibits metal-insulator transition at critical point U_c = 0, where local entanglement reaches its maximum value. Moreover, a transition between charge- and spin-density- wave (CDW-SDW) occurs in 1D Extended Hubbard Model tUV with long-range interaction at straight line U = 2 V. The analysis of our obtained results shows that CDW-SDW transition has curious properties whose can be used in quantum information processing.

     

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 U_c≈W. We discuss the significance 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.     

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     

Magnetic collapse and electronic phase transitions at high pressure in transition metal oxides

A review of electronic and magnetic phase transition in metal oxides with strong electron correlations (SEC) is given. The bandwidth control of the insulator gap is expected in the Hubbard model when the decreasing of the interatomic distance results in the bandwidth W(P) increase and at some critical value P_c, W(P_c)∼U and the Mott–Hubbard gap disappears. The other situation takes place in transition metal boroxides FeBO₃ and GdFe₃(BO₃)₄, where the increase of crystal field parameter Δ(P) results in the high spin–low spin crossover.     

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.     

Mott transition in the asymmetric Hubbard model at half-filling within dynamical mean-field theory

The asymmetric Hubbard model with hopping integrals dependent on an electron spin (particle sort) is studied using an approximate analytic method within the dynamical mean-field theory. The equations of motion for Hubbard operators followed by projecting and different-time decoupling are used for solving the single-site problem. Particle spectra are investigated at half-filling within various approximations (Hubbard-I, alloy-analogy and a generalization of the Hubbard-III approximation). At half-filling these approximations can describe only continuous gap opening in the spectrum. The approach is used to describe the system between two limit cases (the Falicov-Kimball model and the standard Hubbard model) with continuous transition where U_c is dependent on the value of hopping parameters of different particles.     

Mott-Hubbard transition and antiferromagnetism on the honeycomb lattice

The Hubbard model is investigated for a halffilled honeycomb lattice, using a variational method. Two trial wave functions are introduced, the Gutzwiller wave function, well suited for describing the “metallic” phase at small U and a complementary wave function for the insulating regime at large values of U. The comparison of the two variational ground states at the mean-field level yields a Mott transition at U _c /t ≈ 5:3. In addition, a variational Monte Carlo calculation is performed in order to locate the instability of the “metallic” wave function with respect to antiferromagnetism. The critical value U _m/t ≈ 3:7 obtained in this way is considered to be a lower bound for the true critical point for antiferromagnetism, whereas there are good arguments that the mean-field value U _c/t ≈ 5:3 represents an upper bound for the Mott transition. Therefore the “metal”- insulator transition for the honeycomb lattice may indeed be simultaneously driven by the antiferromagnetic instability and the Mott phenomenon.     

Interaction induced delocalization of two particles: large system size calculations and dependence on interaction strength

The localization length L₂ of two interacting particles in a one-dimensional disordered system is studied for very large system sizes by an efficient and accurate variant of the Green function method. The numerical results (at the band center) can be well described by the functional form L ₂ =L ₁ [0.5+c(U) L ₁ ] where L₁ is the one-particle localization length and the coefficient depends on the strength U of the on-site Hubbard interaction. The Breit-Wigner width or equivalently the (inverse) life time of non-interacting pair states is analytically calculated for small disorder and taking into account the energy dependence of the one-particle localization length. This provides a consistent theoretical explanation of the numerically found U-dependence of c(U). Received 16 September 1998     

Spin fluctuations and ferromagnetic order in two-dimensional itinerant systems with Van Hove singularities

The quasistatic approach is used to analyze the criterion of ferromagnetism for two-dimensional (2D) systems with the Fermi level near Van Hove (VH) singularities of the electron spectrum. It is shown that the spectrum of spin excitations (paramagnons) is positively defined when the interaction between electrons and paramagnons, determined by the Hubbard on-site repulsion U, is sufficiently large. Due to incommensurate spin fluctuations near the ferromagnetic quantum phase transition, the critical interaction U_c remains finite at VH filling and exceeds considerably its value obtained from the Stoner criterion. A comparison with the functional renormalization group results and mean-field approximation which yields a phase separation is also performed.     

Mott-Hubbard transition in a magnetic field

We study the density of states (DOS) as a function of the interaction U in the half-filled simplified Hubbard model in a magnetic field. This model is considered on the Bethe lattice in the limit of high dimensions. We show that the DOS can be calculated exactly, and that many of its properties have an astonishingly simple form. In particular, the DOS can be investigated explicitly in the limits of weak and strong coupling and near the metal-insulator transition. E.g., we find an explicit result for the critical value U_c, at which the metal-insulator transition occurs, as a function of the magnetization. The relation between the magnetization and the magnetic field is calculated numerically. An important result is that the metal-insulator transition, occurring in the model with B = 0, is continuously connected to the metal-insulator transition in the subspace of single spin flips.     

Quantum critical phenomena, entanglement entropy and Hubbard model in 1d with the boundary site with a negative chemical potential −p and the Hubbard coupling U positive

Recently the ground state and some excited states of the half-filled case of the 1d Hubbard model were discussed exactly for an open chain with L sites. The case when the boundary site has the chemical potential −p and the Hubbard coupling U is positive was considered. We model CeAl₂ nanoparticles, in which a valence of 4f electron number changes on surface Ce atoms, by this Hubbard model. A surface phase transition exists at some critical value pc3 of chemical potential (its absolute value) p in the model; when p<pc3 all the charge excitations have the gap, while there exists a massless charge mode when p>pc3. The aim of this Letter is to find whether this surface phase transition is of the first order or of the second order. We have found that the entanglement entropy and its derivative has a discontinuity at pc3 in general and thus this transition is of the first order (with exception of two points for the probability w₂ of occurrence of two electrons with opposites spins on the same site). There is a divergence in the difference of entanglement entropy for points w₂=0 and . The first point w₂=0 corresponds to ferro- (antiferro-) magnetic state at half-filled case. The second point does not correspond to any state for halffilled case. In the first case there is present the surface phase transition of the second order type.     

First and second order ferromagnetic transition at in a 1D itinerant system

We consider a modified version of the one-dimensional Hubbard model, the t ₁ - t ₂ Hubbard chain, which includes an additional next-nearest-neighbor hopping. It has been shown that at weak coupling this model has a Luttinger liquid phase or a spin liquid phase depending upon the ratio of t₂ to t₁. Additionally if the on-site interaction U is large enough, the ground state is fully polarized. Using exact diagonalization and the density-matrix renormalization group, we show that the transition to the ferromagnetic phase is either of first or second order depending on whether the Luttinger liquid or spin liquid is being destabilized. Since we work at T =0, the second order transition is a quantum magnetic critical point. Received 21 July 1999     

Monte-Carlo algorithm for a two-dimensional Hubbard model of high-T c superconductivity

A Monte-Carlo procedure is given for the two-dimensional (2-D) Hubbard model using the Suzuki-Trotter transformation. The resulting three-dimensional (3-D) classical model does not have the usual problems with negative transition probabilities in the large-U limit (U-repulsive interactions). Numerical simulations based on the algorithm described are expected to be of importance for the theory of high-T _c superconductivity.     

Mott-insulator-superfluid-liquid transition in a one-dimensional bosonic Hubbard model: Quantum Monte Carlo method

The values of the insulator gap Δ in one-dimensional systems of interacting bosons described by the Hubbard Hamiltonian are calculated at low temperatures by the quantum world-line Monte Carlo algorithm. The dependence of Δ on the size of the system, the temperature, and the parameters of the model is investigated. It is shown that a chain with N _a=50 sites is already sufficient to estimate the thermodynamic value of the critical quantity (t/U)_c for which a transition from the insulator into the superfluid state occurs in a commensurate system. To within the computational error, this value, (t/U)_c=0.300±0.005, agrees with the value (t/U)_c=0.304±0.002 obtained previously by the combined “exact diagonalization + renormalization-group analysis” method. The characteristic Kosterlitz-Thouless behavior of the insulator gap is demonstrated near the critical region: Δ∼exp[−b(1−t/t _c)^−1/2]. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 2, 92–96 (25 July 1996)     

针对电子极化子迁移的哈伯德U修正受限密度泛函理论方法：TiO2实例研究

极化子的形成和迁移对过渡金属氧化物的物理和化学性质有重要影响. 含哈伯德$U$修正的密度泛函理论和受限密度泛函理论方法经常被应用于小极化子迁移性质的理论研究. 本文在投影缀加波框架中实现了哈伯德$U$修正的受限密度泛函理论(cDFT+U),并将其应用于体相TiO₂中的极化子迁移性质的计算. 确认了哈伯德U的取值对极化子性质的理论预测有重要影响. 采用基于cDFT计算所获得的哈伯德U值,可对TiO₂金红石和锐钛矿相中的极化子性质获得与实验符合很好的描述. 本文表明,使用与理论上一致的方式计算获得的哈伯德U值,cDFT+U有望成为一种有效的不需经验输入而计算过渡金属氧化物极化子性质的第一性原理方法.     

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.     

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.     

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.     

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.     

Ground-state properties of the one-dimensional extended Hubbard model at half filling

The density-matrix renormalization group (DMRG) technique is used to study the ground-state properties of the one-dimensional half-filled Hubbard model with on-site (nearest-neighbor) repulsive interaction U (V) and nearest-neighbor hopping t. We calculate the static spin structure factor to consider the spin degrees of freedom. We notice a striking difference of the static spin structure factor among the spin-density-wave, charge-density-wave (CDW), and bond-order-wave (BOW) phases. Based on the results, we identify the BOW-CDW transition at small (large) U value as continuous (of first order). We also calculate the double occupancy to consider the charge degrees of freedom. For large U, the double occupancy show a discontinuous jump at the BOW-CDW critical point and it implies first-order transition. With decreasing U, the jump becomes smaller and vanishes at the tricritical point U_t≈5.961t. This value is close to our previous estimation U_t=5.89t obtained with other quantities. Consequently, the results of static spin structure factor and double occupancy support the accuracy of our ground-state phase diagram.