Spectral functions in the two-dimensional Hubbard model within a spin-charge rotating frame approach

We have performed electronic spectral function calculations for the Hubbard model on the square lattice using recently developed quantum SU(2) × U(1) rotor approach that enables a self-consistent treatment of the antiferromagnetic state. The collective variables for charge and spin are isolated in the form of the space-time fluctuating U(1) phase field and rotating spin quantization axis governed by the SU(2) symmetry, respectively. As a result interacting electrons appear as composite objects consisting of bare fermions with attached U(1) and SU(2) gauge fields. This allows us to write the fermion Green’s function in the space-time domain as a product of the SU(2) gauge fields, U(1) phase propagator and the pseudo-fermion correlation function. Consequently, the calculation of the spectral line shapes now reduces to performing the convolution of spin, charge and pseudo-fermion Green’s functions. The collective spin and charge fluctuations are governed by the effective actions that are derived from the Hubbard model for any value of the Coulomb interaction. The emergence of a sharp peak in the electron spectral function in the antiferromagnetic state indicates the decay of the electron into separate spin and charge carrying particle excitations.     

Investigation on the Ground State of the Hubbard Model

The absolute ground states of the Hubbard model are explicitly presented within the framework of pseudospin when U > 2μ and U < 2μ. It is shown that the states do not possess true off-diagonal long-range order in the two cases. It is also discovered that in the ground states the U(1) phase symmetry of the Hubbard model is spontaneously broken away from the half-filling, and the total spin is zero, which is independent of the sign of U and the electron filling in the considered periodic lattice.     

First-order pairing transition and single-particle spectral function in the attractive hubbard model

A dynamical mean-field theory analysis of the attractive Hubbard model in the normal phase is carried out upon restricting to solutions where superconducting order is not allowed. A clear first-order pairing transition as a function of the coupling takes place at all the electron densities out of half filling between a Fermi liquid, stable for UU(c), and it is accompanied by phase separation. The spectral function in the metallic phase is constituted by a low-energy structure around the Fermi level, which disappears discontinuously at U = U(c), and two high-energy features (Hubbard bands), which persist in the insulating phase.     

The Hubbard model extended by nearest‐neighbor Coulomb and exchange interaction on a cubic cluster – rigorous and exact results

The Hubbard model on a cube was revisited and extended by both nearest‐neighbor Coulomb correlation W and nearest‐neighbor Heisenberg exchange J. The complete eigensystem was computed exactly for all electron occupancies and all model parameters ranging from minus infinity to plus infinity. For two electrons on the cluster the eigensystem is given in analytical form. For six electrons and infinite on‐site correlation U we determinded the groundstate and the groundstate energy of the pure Hubbard model analytically. For fixed electron numbers we found a multitude of ground state level crossings depending on the various model parameters. Furthermore the groundstates of the pure Hubbard model in dependence on a magnetic field h coupled to the spins are shown for the complete U‐h plane. The critical magnetic field, where the zero spin groundstate breaks down is given for four and six electrons. Suprisingly we found parameter regions, where the ground state spin does not depend monotonously on J in the extended model. For the cubic cluster gas, i.e. an ensemble of clusters coupled to an electron bath, we calculated the density n (μ, T, h) and the thermodynamical density of states from the grand potential. The ground states and the various spin‐spin correlation functions are studied for both attractive and repulsive values of the three interaction constants. We determined the various anomalous degeneration lines, where n (μ, T = 0, h = 0) shows steps higher than one, since in this parameter regions exotic phenomena as phase separation are to expect in extended models. For the cases where these lines end in triple points, i.e. groundstates of three different occupation numbers are degenerated, we give the related parameter values. Regarding the influence of the nn‐exchange and the nn‐Coulomb correlation onto the anomalous degeneration we find both lifting and inducing of degeneracies depending on the parameter values.     

Correlation effects in quantum spin-Hall insulators: a quantum Monte Carlo study

We consider the Kane-Mele model supplemented by a Hubbard U term. The phase diagram is mapped out using projective auxiliary field quantum Monte Carlo simulations. The quantum spin liquid of the Hubbard model is robust against weak spin-orbit interaction, and is not adiabatically connected to the spin-Hall insulating state. Beyond a critical value of U>U(c) both states are unstable toward magnetic ordering. In the quantum spin-Hall state we study the spin, charge, and single-particle dynamics of the helical Luttinger liquid by retaining the Hubbard interaction only on a ribbon edge. The Hubbard interaction greatly suppresses charge currents along the edge and promotes edge magnetism but leaves the single-particle signatures of the helical liquid intact.     

Non-equilibrium STLS approach to transport properties of single impurity Anderson model

In this work, using the non-equilibrium Keldysh formalism, we study the effects of the electron–electron interaction and the electron-spin correlation on the non-equilibrium Kondo effect and the transport properties of the symmetric single impurity Anderson model (SIAM) at zero temperature by generalizing the self-consistent method of Singwi, Tosi, Land, and Sjolander (STLS) for a single-band tight-binding model with Hubbard type interaction to out of equilibrium steady-states. We at first determine in a self-consistent manner the non-equilibrium spin correlation function, the effective Hubbard interaction, and the double-occupancy at the impurity site. Then, using the non-equilibrium STLS spin polarization function in the non-equilibrium formalism of the iterative perturbation theory (IPT) of Yosida and Yamada, and Horvatic and Zlatic, we compute the spectral density, the current–voltage characteristics and the differential conductance as functions of the applied bias and the strength of on-site Hubbard interaction. We compare our spectral densities at zero bias with the results of numerical renormalization group (NRG) and depict the effects of the electron–electron interaction and electron-spin correlation at the impurity site on the aforementioned properties by comparing our numerical result with the order U²$U^2$ IPT. Finally, we show that the obtained numerical results on the differential conductance have a quadratic universal scaling behavior and the resulting Kondo temperature shows an exponential behavior.     

Cold attractive spin polarized Fermi lattice gases and the doped positive U Hubbard model

Experiments on polarized fermion gases performed by trapping ultracold atoms in optical lattices allow the study of an attractive Hubbard model for which the strength of the on-site interaction is tuned by means of a Feshbach resonance. Using a well-known particle-hole transformation we discuss how results obtained for this system can be reinterpreted in the context of a doped repulsive Hubbard model. In particular, we show that the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state corresponds to the striped state of the two-dimensional doped positive U Hubbard model. We then use the results of numerical studies of the striped state to relate the periodicity of the FFLO state to the spin polarization. We also comment on the relationship of the d(x(2)-y(2)) superconducting phase of the doped 2D repulsive Hubbard model to a d-wave spin density wave state for the attractive case.     

An effective quantum parameter for strongly correlated metallic ferromagnets

The correlated motion of electrons in metallic ferromagnets is investigated in terms of a realistic interacting-electron model with N-fold orbital degeneracy and intra-orbital (U) and inter-orbital (J) Coulomb interactions. Correlation-induced self-energy and vertex corrections are incorporated systematically to provide a non-perturbative Goldstone-mode-preserving scheme. An effective quantum parameter [U2+(N-1)J2]/[U+(N-1)J]2 is obtained which determines, in analogy with 1/S for quantum spin systems and 1/N for the N-orbital Hubbard model, the strength of correlation-induced quantum corrections to magnetic excitations. The rapid suppression of this quantum parameter with Hund's coupling J, especially for large N, provides fundamental insight into the phenomenon of strong stabilization of metallic ferromagnetism by orbital degeneracy and Hund's coupling. Correlation effects are investigated for spin stiffness, magnon dispersion, electronic spectral function, density of states, and finite-temperature spin dynamics using realistic bandwidth, interaction, and lattice parameters for iron.     

Thermodynamics of a 4‐site Hubbard model by analytical diagonalization

By use of the conservation laws a four‐site Hubbard model coupled to a particle bath within an external magnetic field in z‐direction was diagonalized. The analytical dependence of both the eigenvalues and the eigenstates on the interaction strength, the chemical potential and magnetic field was calculated. It is demonstrated that the low temperature behaviour is determined by a delicate interplay between many‐particle states differing in electron number and spin if the electron density is away from half‐filling. The grand partition sum is calculated and the specific heat, the susceptibility as well as various correlation functions and spectral functions are given in dependence of the interaction strength, the electron occupation and the applied magnetic field. For both the grand canonical and the canonical ensemble the high‐temperature crossing points of the specific heat are calculated. Whereas in the weak correlation regime the universal value calculated by second order perturbation theory for several Hubbard systems being in the thermodynamic limit is confirmed, these crossing points vanish for intermediate to strong correlation.     

Electron spectrum in high-temperature cuprate superconductors

A microscopic theory for the electron spectrum of the CuO₂ plane within an effective p-d Hubbard model is proposed. The Dyson equation for the single-electron Green’s function in terms of the Hubbard operators is derived and solved self-consistently for the self-energy evaluated in the noncrossing approximation. Electron scattering on spin fluctuations induced by the kinematic interaction is described by a dynamical spin susceptibility with a continuous spectrum. The doping and temperature dependence of electron dispersions, spectral functions, the Fermi surface, and the coupling constant λ are studied in the hole-doped case. At low doping, an arc-type Fermi surface and a pseudogap in the spectral function close to the Brillouin zone boundary are observed. The text was submitted by the authors in English.     

Incommmensurability and unconventional superconductor to insulator transition in the hubbard model with bond-charge interaction

We determine the quantum phase diagram of the one-dimensional Hubbard model with bond-charge interaction X in addition to the usual Coulomb repulsion U>0 at half-filling. For large enough X相似文献   

Intermediate phase of the one dimensional half-filled Hubbard-Holstein model

We present a numerical study of the Hubbard-Holstein model in one dimension at half filling, including finite-frequency quantum phonons. At half filling, the effects of the electron-phonon and electron-electron interactions compete with the Holstein phonon coupling acting as an effective negative Hubbard on-site interaction U that promotes on-site electron pairs and a Peierls charge-density wave state. Most previous work on this model has assumed that only Peierls or Mott phases are possible at half filling. However, there has been speculation that a third metallic phase exists between the Peierls and Mott phases. We confirm the intermediate phase, and show that the Luttinger liquid correlation exponent K(rho) >1 in this region, indicating dominant superconducting pair correlations. We explore the full phase diagram as a function of Hubbard U, phonon coupling constant, and phonon frequency.     

U(1) gauge theory of the Hubbard model: spin liquid states and possible application to kappa-(BEDT-TTF)2Cu2(CN)3

We formulate a U(1) gauge theory of the Hubbard model in the slave-rotor representation. From this formalism it is argued that spin liquid phases may exist near the Mott transition in the Hubbard model on triangular and honeycomb lattices at half filling. The organic compound kappa-(BEDT-TTF)2Cu2(CN)3 is a good candidate for the spin liquid state on a triangular lattice. We predict a highly unusual temperature dependence for the thermal conductivity of this material.     

Fluctuation-exchange study of antiferromagnetism in disordered electron-doped cuprate superconductors

On the basis of the Hubbard model, we extend the fluctuation-exchange (FLEX) approach to investigating the properties of the antiferromagnetic (AF) phase in electron-doped cuprate superconductors. Furthermore, by incorporating the effect of scatterings due to the disordered dopant atoms into the FLEX formalism, our numerical results show that the antiferromagnetic transition temperature, the onset temperature of pseudogap due to spin fluctuations, the spectral density of the single particle near the Fermi surface, and the staggered magnetization in the AF phase as a function of electron doping can consistently account for the experimental measurements.     

Effects of interaction on quantum spin Hall insulators

We study the S(z)-conserving quantum spin Hall insulator in the presence of Hubbard U from a field theory point of view. The main findings are the following. (1) For arbitrarily small U the edges possess power-law correlated antiferromagnetic XY local moments. Gapless charge excitations arise from the Goldstone-Wilczek mechanism. (2) Electron tunneling between opposite edges allows vortex instantons to proliferate when K, the XY stiffness constant, satisfies 4πK+(4πK)(-1)<4. When the preceding inequality is violated, the edge modes remain gapless despite the sample width being finite. (3) The phase transition from the topological insulator to the large U antiferromagnetic insulator is triggered by the condensation of magnetic excitons. (4) In the large U antiferromagnetic insulating phase the magnetic vortices carry charges proportional to the square magnitude of the antiferromagnetic order parameter.     

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.     

Ground-state phase diagram of a half-filled one-dimensional extended hubbard model

The density-matrix renormalization group is used to study the phase diagram of the one-dimensional half-filled Hubbard model with on-site (U) and nearest-neighbor (V) repulsion and hopping t. A critical line V(c)(U) approximately U/2 separates a Mott insulating phase from a charge-density-wave phase. The formation of bound charge excitations for V>2t changes the phase transition from continuous to first-order at a tricritical point U(t) approximately 3.7t, V(t)=2t. A frustrating effective antiferromagnetic spin coupling induces a bond-order-wave phase on the critical line V(c)(U) for U(t)相似文献   

SU(2) gauge theory of the Hubbard model: emergence of an anomalous metallic phase near the Mott critical point

We propose one possible mechanism for an anomalous metallic phase appearing frequently in two spatial dimensions, that is, local pairing fluctuations. Introducing a pair-rotor representation to decompose bare electrons into collective pairing excitations and renormalized electrons, we derive an SU(2) gauge theory of the Hubbard model as an extended version of its U(1) gauge theory. Since our effective SU(2) gauge theory admits two kinds of collective bosons corresponding to pair excitations and density fluctuations, respectively, an intermediate phase appears naturally between the spin liquid Mott insulator and Fermi liquid metal of the U(1) gauge theory, characterized by softening of density-fluctuation modes as the Fermi liquid, but gapping of pair-excitation modes. We show that this intermediate phase is identified with an anomalous metallic phase because there are no electronlike quasiparticles although it is metallic.