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.

     

Fourth-order perturbation theory for the half-filled Hubbard model in infinite dimensions

We calculate the zero-temperature self-energy to fourth-order perturbation theory in the Hubbard interaction U for the half-filled Hubbard model in infinite dimensions. For the Bethe lattice with bare bandwidth W, we compare our perturbative results for the self-energy, the single-particle density of states, and the momentum distribution to those from approximate analytical and numerical studies of the model. Results for the density of states from perturbation theory at U/W = 0.4 agree very well with those from the Dynamical Mean-Field Theory treated with the Fixed-Energy Exact Diagonalization and with the Dynamical Density-Matrix Renormalization Group. In contrast, our results reveal the limited resolution of the Numerical Renormalization Group approach in treating the Hubbard bands. The momentum distributions from all approximate studies of the model are very similar in the regime where perturbation theory is applicable, . Iterated Perturbation Theory overestimates the quasiparticle weight above such moderate interaction strengths.Received: 9 September 2003, Published online: 30 January 2004PACS: 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 71.27. + a Strongly correlated electron systems; heavy fermions - 71.30. + h Metal-insulator transitions and other electronic transitions     

Normal phase and superconducting instability in the attractive Hubbard model: a DMFT(NRG) study

We study the normal (nonsuperconducting) phase of the attractive Hubbard model within the dynamical mean field theory (DMFT) using the numerical renormalization group (NRG) as an impurity solver. A wide range of attractive potentials U is considered, from the weak-coupling limit, where superconducting instability is well described by the BCS approximation, to the strong-coupling region, where the superconducting transition is described by Bose condensation of compact Cooper pairs, which are formed at temperatures much exceeding the superconducting transition temperature. We calculate the density of states, the spectral density, and the optical conductivity in the normal phase for this wide range of U, including the disorder effects. We also present the results on superconducting instability of the normal state dependence on the attraction strength U and the degree of disorder. The disorder influence on the critical temperature T _c is rather weak, suggesting in fact the validity of Anderson’s theorem, with the account of the general widening of the conduction band due to disorder.     

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.     

Fermi-liquid quasi-particles and -superconductivity in the two-dimensional Hubbard model

A frequency- and momentum-renormalization-group acceleration together with an analytical approach is used to obtain the retarded Green's function in the self-consistent and conserving fluctuation-exchange (FLEX) approximation for the two-dimensional Hubbard model in the normal state and in the superconducting state. The analytical expressions for this approach are given. For band-fillings near half filling the self-energy in the normal state exhibits Fermi-liquid behaviour for, low temperatures and frequencies near the chemical potential, if the momentum is chosen near the Fermi-surface. However due to the presence of large many body effects the observed Fermi-liquid region near the chemical potential and near the Fermi-surface is very small. Results for the single particle density of states, the occupation number and the spectral function are presented. The superconducting state with symmetry is obtained for U = 2 to U = 6 and a (U, n)-phase diagram for the transition temperature T_c is presented. A maximum T_c/t of 0.0275 is obtained for U = 6 near half filling.     

“Linearized” dynamical mean-field theory for the Mott-Hubbard transition

The Mott-Hubbard metal-insulator transition is studied within a simplified version of the Dynamical Mean-Field Theory (DMFT) in which the coupling between the impurity level and the conduction band is approximated by a single pole at the Fermi energy. In this approach, the DMFT equations are linearized, and the value for the critical Coulomb repulsion can be calculated analytically. For the symmetric single-band Hubbard model at zero temperature, the critical value is found to be given by 6 times the square root of the second moment of the free (U=0) density of states. This result is in good agreement with the numerical value obtained from the Projective Selfconsistent Method and recent Numerical Renormalization Group calculations for the Bethe and the hypercubic lattice in infinite dimensions. The generalization to more complicated lattices is discussed. The “linearized DMFT” yields plausible results for the complete geometry dependence of the critical interaction. Received 6 May 1999 and Received in final form 2 July 1999     

Hartree-Fock theory of spiral magnetic order in the 2-d Hubbard model

The magnetic order in the 2-d Hubbard model is investigated within Hartree-Fock theory. For the class of states with uniform particle density and spiral arrangement of spins the phase diagram is obtained by minimizing the free energy. At zero temperature and large Hubbard interactionU there is a continuous transition from the antiferromagnetic solution at half filling over a spiral state of increasing wavelength along the diagonal of the lattice to the ferromagnetic state at doping _c 2t/U. At finite temperatureT, the antiferromagnetic state remains stable for doping smaller than _AF 2T/U. For intermediate values ofU and finite doping there exists also a phase with a spiral wave vector of the form Q=(Q, ).     

Disorder effects in the BCS-BEC crossover region of the attractive Hubbard model

We study the disorder effects upon superconducting transition temperature T _c and the number of local pairs within the attractive Hubbard model in the combined Nozieres-Schmitt-Rink and DMFT + Σ approximations. We analyze the wide range of attractive interaction U, from the weak coupling region, where instability of the normal phase and superconductivity are well described by the BCS model, to the limit of strong coupling, where superconducting transition is determined by Bose-Einstein condensation of compact Cooper pairs, forming at temperatures much higher than superconducting transition temperature. It is shown that disorder can either suppress T _c in the weak coupling limit, or significantly enhance T _c in the case of strong coupling. However, in all cases we actually prove the validity of generalized Anderson theorem, so that all changes in T _c are related to change in the effective bandwidth due to disorder. Similarly, disorder effects on the number of local pairs are only due to these band-broadening effects.     

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.     

Finite temperature neutral-ionic transition and lattice dimerization in charge-transfer complexes: QMC study

We numerically investigate the neutral-ionic (NI) phase transition on the basis of the ionic extended Hubbard model with electron-lattice coupling as well as inter-chain Coulomb interaction. Finite-temperature (T) phase transitions are examined by a quantum Monte Carlo method, within adiabatic approximation for the lattice displacement together with inter-chain mean-field treatment. The NI transition either with or without the electron-lattice coupling is of first-order at low-T and transforms into a cross-over regime with increasing T. We confirm there exist two phases in the ionic region: with and without lattice dimerization, as suggested in recent experiments. The former is ferroelectric, which is rooted in the Coulomb interactions and a spin-Peierls mechanism.     

Triplet superconductivity vs. easy-plane ferromagnetism in a 1D itinerant electron system with transverse spin anisotropy

In this paper we study the ground state phase diagram of a one-dimensional t-U-J model, at half-filling. In the large-bandwidth limit and for ferromagnetic exchange with easy-plane anisotropy, a phase with gapless charge and massive spin excitations, characterized by the coexistence of triplet superconducting and spin density wave instabilities is realized in the ground state. With reduction of the bandwidth, a transition into an insulating phase showing properties of the spin- XY model takes place.Received: 6 February 2004, Published online: 9 April 2004PACS: 71.10.Hf Non-Fermi-liquid ground states, electron phase diagrams and phase transitions in model systems - 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 74.20.Mn Nonconventional mechanisms (spin fluctuations, polarons and bipolarons, resonating valence bond model, anyon mechanism, marginal Fermi liquid, Luttinger liquid, etc.) - 71.27. + a Strongly correlated electron systems; heavy fermions - 75.10.Pq Spin chain modelsG.I. Japaridze: Permanent address: Andronikashvili Institute of Physics, Georgian Academy, Tamarashvili 6, Tbilisi 380077, Georgia     

Can a Metal-Insulator Transition Induce s-Wave Superconductivity?

A recent paper of Capone et al. has studied an extended Hubbard model, in which local orbital degrees of freedom allow an even integer occupation at each site. A strong local repulsion U triggers a metal-insulator transition. Within a DMFT numerical analysis they show that when the ground state is a singlet a pocket of s-wave superconductivity appears in the vicinity of the Mott transition, with a strongly enhanced superconducting gap. A qualitative understanding of their result is proposed, and suggestions are made of possible systems in which this beautiful effect might be searched.     

Strong-coupling perturbation theory of the Hubbard model

The strong-coupling perturbation theory of the Hubbard model is presented and carried out to order (t/U)⁵ for the one-particle Green function in arbitrary dimension. The spectral weight is expressed as a Jacobi continued fraction and compared with new Monte-Carlo data of the one-dimensional, half-filled Hubbard model. Different regimes (insulator, conductor and short-range antiferromagnet) are identified in the temperature-hopping integral (T,t) plane. This work completes a first paper on the subject (Phys. Rev. Lett. 80, 5389 (1998)) by providing details on diagrammatic rules and higher-order results. In addition, the non half-filled case, infinite resummations of diagrams and the double occupancy are discussed. Various tests of the method are also presented. Received 25 October 1999     

Exact solution of the simplified hubbard model

We present the exact solution of the simplified Hubbard model in which only one kind of electrons can hop and this quantum mechanical hopping of electrons is assumed to be unconstrained. It is shown that the model still behaves nontrivially, although it no longer depends on the lattice structure and the dimensionality of the system. For this case we find: (i) a gap in the ground state energy always exists at the half-filled band point (n=1), (ii) a preferred magnetic state atn=1 and largeU is a total spin singlet, (iii)U-dependence of the ground state energy has qualitatively the same form as one of the conventional Hubbard model with the (t ²/U)-behavior at largeU. A phase diagram of the model is discussed.     

Hydrostatic pressure driven spin,volume and band gap collapses in SmFeO3: a GGA + U study

The crystal structure, magnetic and electronic properties of SmFeO₃ under hydrostatic pressure have been studied by first-principles calculations within the generalized gradient approximation plus Hubbard U (GGA + U). The iso-structural phase transition with spin, volume and band gap collapses can be induced by a large enough hydrostatic pressure. The high-spin (HS) state of Fe³⁺, with the magnetic moment of ~4 μ_B, is retained at low pressure. The spin crossover occurs at a transition pressure (~68 GPa) with the magnetic moment of Fe³⁺ decreasing to ~1 μ_B in low-spin (LS) state. Meanwhile, the reductions of cell volume (by ~?5.43%) and band gap (from >2 eV to ~1.6 eV) of SmFeO₃ are obtained when the HS–LS transition happens. Finally, the critical pressure of HS–LS transition, magnetic and electronic properties are found to be Hubbard U dependent.     

Metal-insulator transition in the Hubbard model: a simple description including the Kondo effect

The electron spectrum structure in the half-filled Hubbard model is considered in terms of the one-particle Greens functions within many-electron representation. A simple analytical generalization of the single-site Hubbard-III approximation is obtained, which takes into account the Fermi excitations (Kondo terms). The problem of the metal-insulator transition in the paramagnetic phase is investigated. The occurrence of a three-peak density-of-states structure including the Kondo peak at the Fermi level is discussed. A comparison with large-d calculations is performed.Received: 5 January 2004, Published online: 8 June 2004PACS:   71.10.Fd Lattice fermion models (Hubbard model, etc.) - 71.27. + a Strongly correlated electron systems; heavy fermions - 71.30. + h Metal-insulator transitions and other electronic transitions     

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.     

Ginzburg-Landau Expansion and the Upper Critical Field in the Disordered Attractive Hubbard Model (Brief Review)

We present a brief review of our studies of disorder influence upon Ginzburg-Landau expansion coefficients in Anderson-Hubbard model with attraction in the framework of the generalized DMFT + Σ approximation. A wide range of attractive potentials U is considered from weak coupling limit, where superconductivity is described by BCS model, to the limit of very strong coupling, where superconducting transition is related to the Bose-Einstein condensation of compact Cooper pairs, which are formed at temperatures significantly higher than the superconducting transition temperature, as well as the wide range of disorders from weak to strong, when the system is in the vicinity of Anderson transition. For the same range of parameters we study in detail the temperature behavior of orbital and paramagnetic upper critical field H_c2(T), which demonstrates the anomalies due both to the growth of attractive potential and to the effects of strong disordering.