Non-Fermi-liquid phases in the two-band Hubbard model: finite-temperature exact diagonalization study of Hund's rule coupling

The two-band Hubbard model involving subbands of different widths is investigated via finite-temperature exact diagonalization (ED) and dynamical mean field theory (DMFT). In contrast to the quantum Monte Carlo (QMC) method which at low temperatures includes only Ising-like exchange interactions to avoid sign problems, ED permits a treatment of Hund's exchange and other onsite Coulomb interactions on the same footing. The role of finite-size effects caused by the limited number of bath levels in this scheme is studied by analyzing the low-frequency behavior of the subband self-energies as a function of temperature, and by comparing with numerical renormalization group (NRG) results for a simplified effective model. For half-filled, non-hybridizing bands, the metallic and insulating phases are separated by an intermediate mixed phase with an insulating narrow and a bad-metallic wide subband. The wide band in this phase exhibits different degrees of non-Fermi-liquid behavior, depending on the treatment of exchange interactions. Whereas for complete Hund's coupling, infinite lifetime is found at the Fermi level, in the absence of spin-flip and pair-exchange, this lifetime becomes finite. Excellent agreement is obtained both with new NRG and previous QMC/DMFT calculations. These results suggest that-finite temperature ED/DMFT might be a useful scheme for realistic multi-band materials.     

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.     

Modular invariant partition function of the Hubbard model

Summary By making use of the Abelian bosonization procedure, we obtain a Coulomb-gas picture of the continuum limit of the one-dimensional Hubbard model. It is shown clearly that the semi-direct product of two Virasoro algebras (c=1) denotes symmetry of excitations of the Hubbard model. A systematic study of modular invariant partition function for the Hubbard model is presented. Correlation functions are calculated explicitly and the result is in good agreement with those of numerical simulations and Tomonaga-Luttinger model.     

Variational approach to spin fluctuations in the Hubbard model

We study a one parameter variational wave function to improve the spin density wave ground state of the Hubbard model by inclusion of quantum spin fluctuations. Using a perturbative approach and novel lattice summation techniques we present analytical as well as numerical results for the correlation energies and the staggered magnetizations in one and two dimensions. We find ground state energies which are satisfyingly close to known exact results and are significantly lower than those of existing Gutzwiller and numerical treatments.     

Ground-state properties of the Falicov-Kimball model in one and two dimensions

A new numerical method is used to study the ground-state properties of the spinless Falicov-Kimball model in one and two dimensions. The resultant solutions are used to examine the phase diagram of the model as well as possibilities for valence and metal-insulator transitions. In one dimension a comprehensive phase diagram of the model is presented. On the base of this phase diagram, the complete picture of valence and metal-insulator transitions is discussed. In two dimensions the structure of ground-state configurations is described for intermediate interactions between f and d electrons. In this region the phase separation and metal-insulator transitions are found at low f-electron concentrations. It is shown that valence transitions exhibit a staircase structure. Received 20 October 2000     

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.     

Renormalized quasiparticles in antiferromagnetic states of the Hubbard model

We analyze the properties of the quasiparticle excitations of metallic antiferromagnetic states in a strongly correlated electron system. The study is based on dynamical mean field theory (DMFT) for the infinite dimensional Hubbard model with antiferromagnetic symmetry breaking. Self-consistent solutions of the DMFT equations are calculated using the numerical renormalization group (NRG). The low energy behavior in these results is then analyzed in terms of renormalized quasiparticles. The parameters for these quasiparticles are calculated directly from the NRG derived self-energy, and also from the low energy fixed point of the effective impurity model. From these the quasiparticle weight and the effective mass are deduced. We show that the main low energy features of the k-resolved spectral density can be understood in terms of the quasiparticle picture. We also find that Luttinger's theorem is satisfied for the total electron number in the doped antiferromagnetic state.     

Dynamical spin and charge response functions in the doped two-dimensional Hubbard model

Dynamical properties of the spin and charge response functions in the doped two-dimensional Hubbard model are calculated by taking into account the drastic separation of the single-particle spectral function into the low-energy coherent and high-energy incoherent parts due to the strong Coulomb interaction. We show that this evolution of the electronic states is the origin of the broad and structureless feature in the charge response function. In the weak coupling regime the low-energy enhancement of the spin excitation is produced which can be explained within the random phase approximation. However, for the larger interaction close to the antiferromagnetic Stoner condition, the low-energy intensity of the spin excitation is suppressed. Received: 25 September 1997 / Revised: 19 December 1997 / Accepted: 9 January 1998     

Exact superconducting ground states of the extended Anderson model

We obtain exact ground states of an extended periodic Anderson model (EPAM) with non-local hybridization and Coulomb repulsion between f and c electrons (Falicov-Kimball term) in one dimension. We show that for a range of parameter values these ground states exhibit composite hole pairing and superconductivity that originate from purely electronic interactions.     

Phase diagram of the Mott transition in a two-band Hubbard model in infinite dimensions

The Mott metal-insulator transition in the two-band Hubbard model in infinite dimensions is studied by using the linearized dynamical mean-field theory recently developed by Bulla and Potthoff. The phase boundary of the metal-insulator transition is obtained analytically as a function of the on-site Coulomb interaction at the d-orbital, the charge-transfer energy between the d- and p-orbitals and the hopping integrals between p-d, d-d and p-p orbitals. The result is in good agreement with the numerical results obtained from the exact diagonalization method. Received 5 October 2000 and Received in final form 8 December 2000     

Connes’ spectral triple and U(1) gauge theory on finite sets

We first apply Connes’ noncommutative geometry to a finite point set. The explicit form of the action functional of U(1) gauge field on this n-point set is obtained. We then construct the U(1) gauge theory on a disconnected manifold consisting of n copies of a given manifold. In this case, the explicit action functional of U(1) gauge field is also obtained.     

A variational treatment of the periodic Anderson model with antiferromagnetic order

We discuss a variational ground state wave function for the symmetric periodic Anderson model with commensurate spin density order. The energy of this ansatz is evaluated in closed form. Our approach generalizes a variational treatment proposed recently by Strack and Vollhardt and results in significantly lower energy. Contrary to the Gutzwiller ansatz the wave function recovers the Schrieffer-Wolff limit for large Coulomb repulsion. We clarify the relation of our approach to unrestricted Hartree-Fock and present a comparison with existing quantum Monte Carlo calculations for one dimension.     

Anomalous U(1) symmetry and sparticles

Using anomalous U(1) symmetry the quark mass texture is determined uniquely. We analyze squark mass spectrum based on the above mass matrices and discuss the possibility to solve the problems of FCNC and CP caused by complex phases of soft terms, including the viewpoint of M theory.     

Magnetism and phase separation in the ground state of the Hubbard model

We discuss the ground state magnetic phase diagram of the Hubbard model off half filling within the dynamical mean-field theory. The effective single-impurity Anderson model is solved by Wilson's numerical renormalization group calculations, adapted to symmetry broken phases. We find a phase separated, antiferromagnetic state up to a critical doping for small and intermediate values of U, but could not stabilize a Néel state for large U and finite doping. At very large U, the phase diagram exhibits an island with a ferromagnetic ground state. Spectral properties in the ordered phases are discussed. Received 9 January 2002 Published online 25 June 2002     

Effective action for D-branes on SU(2)/U(1) gauged WZW model

Dynamics of D-branes on SU(2)/U(1) gauged WZW model are investigated. We find the effective action for infinite k, where k is the level of WZW model. We also consider finite k correction to the effective action which is compatible with Fedosov's deformation quantization of the background.     

Emergence of helicity ±2 modes (gravitons) from qubit models

We construct two quantum qubit models (or quantum spin models) on three-dimensional lattice in space, L-type model and N-type model. We show that, under a controlled approximation, all   the low energy excitations of the L-type model are described by one set of helicity ±2 modes with ω∝k³$\omega \propto k^3$ dispersion. We also argue that all   the low energy excitations of the N-type model are described by one set of helicity ±2 modes with ω∝k$\omega \propto k$ dispersion. In both model, the low energy helicity ±2 modes can be described by a symmetric tensor field _hμν$h_{\mu \nu }$ in continuum limit, and the gaplessness of the helicity ±2 modes is protected by an emergent linearized diffeomorphism gauge symmetry _hμν→_hμν+_∂μfν+_∂νfμ$h_{\mu \nu }\to h_{\mu \nu }+{\partial }_{\mu }{f}_{\nu }+{\partial }_{\nu }{f}_{\mu }$ at low energies. Thus the linearized quantum gravity emerge from our lattice models  . It turns out that the low energy effective Lagrangian density of the L-type model is invariant under the linearized diffeomorphism gauge transformation. Such a property protects the gapless ω∝k³$\omega \propto k^3$ helicity ±2 modes. In contrast, the low energy effective Lagrangian of the N-type model changes by a boundary term under the linearized diffeomorphism gauge transformation. Such a property protects the gapless ω∝k$\omega \propto k$ helicity ±2 modes. From many-body physics point of view, the ground states of the our two qubit model represent new states of quantum matter, whose low energy excitations are all described by one set of gapless helicity ±2 modes.