Local non-abelian gauge symmetry of the Hubbard model

It is shown that the field operators of an electron system on a lattice can be decomposed into direct products of two kinds of operators acting in two separate Hilbert spaces. The Hilbert space of electron states thus becomes a direct product of two Hilbert spaces. By this fact a certain class of electron systems exhibits a formal separation of charge and spin degrees of freedom into two kinds of elementary excitations. A typical example of such a system is given by the Hubbard model. The separation of charge and spin resulting from the new representation of the field operators can be considered as a rigorous realization and generalization of an idea expressed by Anderson concerning the separation of spin and charge degrees of freedom in strongly correlated electron systems. The new representation of electron field operators implies the existence of a localU(2) gauge symmetry in the theory. The theory of superconductivity based on the Hubbard model is then represented by a non-abelian gauge field theory.Dedicated to the memory of my teacher and friend Professor Jozef Kvasnica.The main part of this work has been done during the author stay at the Research Institute for Theoretical Physics, University of Helsinki. The author expresses this sincere gratitude to Prof. C. Cronström, who played an important role in completing this work.     

A field-theoretical approach to the extended Hubbard model

We transform the quartic Hubbard terms in the extended Hubbard model to a quadratic form by making the Hubbard–Stratonovich transformation for the electron operators. This transformation allows us to derive exact results for mass operator and charge–charge and spin–spin correlation functions for s-wave superconductivity. We discuss the application of the method to the d-wave superconductivity.     

Quasi‐particle peak due to magnetic order in strongly correlated electron systems

We study the electron spectral function of the antiferromagnetically ordered phase of the three dimensional Hubbard model, using recently formulated low‐energy theory based on the 2D half‐filled Hubbard model which describes both collective spin and charge fluctuations for arbitrary value of the Coulomb repulsion U. The model then is solved by a saddle‐point approximation within the CP¹ representation for the Neel field. The single‐particle properties are obtained by writing the fermion field in terms of a U(1) phase, Schwinger boson SU(2) fields and a pseudofermion variables. We demonstrate that the appearance of a sharp peak in the electron spectral function in the antiferromagnetic state points to the emergence of the bosonic mode, which is associated with spin ordering.     

Spin fluctuation contribution to the specific heat of strongly correlated fermions

We calculate the free energy of a system of fermions at low temperatures within the Hubbard model using a slave boson representation, which generalizes the approach of Kotliar and Ruckenstein. The mean field approximation is identical to Gutzwiller's solution. The one-loop corrections provide aT ³ lnT spin fluctuation contribution to the specific heat, which reduces for weak coupling to the result of paramagnon theory first derived by Brenig et al.Dedicated to Professor W. Brenig on the occasion of his 60th birthday     

Hubbard model,conserved quantities,and computer algebra

The constants of motion of the half-filled four-point Hubbard model with cyclic boundary conditions are given in Wannier and Bloch representation. The total number operator and total spin operator are conserved and spin-reversal symmetry exists. In Wannier representation we have additionally the C_4v symmetry and in Bloch representation we have the total momentum operator which is conserved. The anticommutation relations for Fermi operators with spin are implemented using computer algebra. Using computer algebra, all the constants of motion are given. The one-dimensional Hubbard model admits a Lax representation. From the Lax pair we find a new constant of motion.     

Equation of motion method for composite field operators

The Greens function formalism in Condensed Matter Physics is reviewed within the equation of motion approach. Composite operators and their Greens functions naturally appear as building blocks of generalized perturbative approaches and require fully self-consistent treatments in order to be properly handled. It is shown how to unambiguously set the representation of the Hilbert space by fixing both the unknown parameters, which appear in the linearized equations of motion and in the spectral weights of non-canonical operators, and the zero-frequency components of Greens functions in a way that algebra and symmetries are preserved. To illustrate this procedure some examples are given: the complete solution of the two-site Hubbard model, the evaluation of spin and charge correlators for a narrow-band Bloch system, the complete solution of the three-site Heisenberg model, and a study of the spin dynamics in the Double-Exchange model.Received: 9 June 2003, Published online: 19 November 2003PACS: 71.10.-w Theories and models of many-electron systems - 71.27. + a Strongly correlated electron systems; heavy fermions - 71.10.Fd Lattice fermion models (Hubbard model, etc.)     

Theory of high-temperature superconductivity in cuprates

A microscopic theory of electronic spectrum and superconducting pairing in the high-temperature cuprate superconductors is presented. The theory is based on consideration of strong electron correlations within the Bogolyubov polar model. The Dyson equation is derived by using the equation of motion method for the thermodynamic Green functions in terms of the Hubbard operators. The self-energy is evaluated in the noncrossing approximation for electron scattering on spin and charge fluctuations induced by kinematic interaction. The theory demonstrates that a strong Coulomb repulsion results in the anomalous electronic spectrum and unconventional (d-wave) superconducting pairing with high T _c mediated by the antiferromagnetic exchange and spin fluctuations.     

Ladder operator for the one-dimensional Hubbard model

The one-dimensional Hubbard model is integrable in the sense that it has an infinite family of conserved currents. We explicitly construct a ladder operator which can be used to iteratively generate all of the conserved current operators. This construction is different from that used for Lorentz invariant systems such as the Heisenberg model. The Hubbard model is not Lorentz invariant, due to the separation of spin and charge excitations. The ladder operator is obtained by a very general formalism which is applicable to any model that can be derived from a solution of the Yang-Baxter equation.     

Pseudogap formation in copper oxide superconductors with inclusion of spin and charge fluctuations

The influence of spin and charge fluctuations on the pseudogap formation in cuprate superconductors has been studied using the diagram technique for Hubbard operators. It has been shown that the joint inclusion of the spin and charge fluctuations leads to the formation of “shadow” bands with a strong modulation of the spectral intensity and to a decrease in the density of electronic states at the Fermi level.     

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.     

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.     

Quantum transport through anisotropic molecular magnets: Hubbard Green function approach

We extend the Green function approach to quantum transport through an anisotropic molecular magnet system with the help of Hubbard operators. Based on the single molecular magnet model, we reformulate the large spin and the total Hamiltonian in the language of Hubbard operators and obtain analytical expressions of the retarded Green function in sequential tunneling and Kondo regimes. In addition to this, we show the connection of our method to the master equation method in sequential regime and discuss a simple isotropic case in Kondo regime, in which we find a three-peak Kondo structure, a feature characterizing the isotropic exchange interaction between the localized electron and large spin.     

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.     

On the theory of superconductivity in the extended Hubbard model

A microscopic theory of superconductivity in the extended Hubbard model which takes into account the intersite Coulomb repulsion and electron-phonon interaction is developed in the limit of strong correlations. The Dyson equation for normal and pair Green functions expressed in terms of the Hubbard operators is derived. The self-energy is obtained in the noncrossing approximation. In the normal state, antiferromagnetic short-range correlations result in the electronic spectrum with a narrow bandwidth. We calculate superconducting T _c by taking into account the pairing mediated by charge and spin fluctuations and phonons. We found the d-wave pairing with high-T _c mediated by spin fluctuations induced by the strong kinematic interaction for the Hubbard operators. Contributions to the d-wave pairing coming from the intersite Coulomb repulsion and phonons turned out to be small.     

Hubbard模型中的相位弦效应与交互Chern-Simons理论

费米子符号在费米液体理论中至关重要. 然而, 在Mott绝缘体中, 很强的电子Coulomb相互作用抑制了体系的电荷涨落并消除了电子交换带来的费米子符号问题. 本文首先回顾二分晶格上Hubbard模型的相位弦理论, 从弱关联的费米液体到强关联的反铁磁Mott绝缘体的转变可以由此得到统一理解. 在任意Coulomb作用强度U下, 我们首先导出Hubbard模型的严格的符号结构. 在小U极限下, 它回到通常的费米子符号; 在大U极限下, 它给出了t-J模型的相位弦符号. 在半满情形下, 我们构造了一种电子分数化的表象, 其中, 电荷子与自旋子通过演生的交互Chern-Simons规范场相互耦合. 由此导出的基态波函数拟设与低能有效理论可以定性刻画Hubbard模型的基态相图. 在弱关联区域, 费米液体的准粒子由电荷子与自旋子的束缚态构成, 其长程相位相干性取决于背景自旋的关联性质. 体系的Mott转变可以通过电荷子打开能隙或是通过自旋子玻色凝聚来实现.     

Optical conductivity in the t − J model

Frequency dependent conductivity σ(ω) is calculated for the t ? J model by applying the memory function technique in terms of the Hubbard operators. The relaxation rate due to electron scattering on spin and charge dynamical fluctuations is calculated and a generalized Drude law for σ(ω) is obtained. For a model with an incoherent spectrum for one-hole excitations we obtain a universal form for frequency dependence of relaxation rate and conductivity in terms of the scaling function γ(ω/kT). The relaxation rate for the t ? J model is quite different from that one for the conventional Hubbard model in the strong coupling limit where it vanishes due to an exact cancellation of the intraband scattering and virtual interband transitions.     

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.     

CHARGE AND SPIN GAPS IN THE DIMERIZED HUBBARD MODEL

By using the bosonization and renormalization group methods, we have studied the low energy physical properties in the one-dimensional dimerized Hubbard model. The formation of charge and spin gaps is investigated both for the half-filled electron band and away from the half-filled band. The scaling laws of the charge and spin gaps with the dimerization parameterΔ and the repulsive interaction strength U are obtained.     

Effective action and meson spectrum in quantum chromodynamics

The low-energy meson spectrum of spin 0 and 1⁺ mesons in one-flavour massive QCD is studied. An invariance property expressed by the anomalous chiral Ward identity is used to set up a low-energy expansion for the symmetric effective action. The propagator matrix corresponding to a certain set of operators is calculated and used to study the meson spectrum in the sector under consideration. The spectrum includes two 0^– mesons, one 0⁺ meson and one 1⁺ meson.Part of this work was carried out while the author was visiting the Department of Mathematics at King's College, London University. The author would like to thank Professor J. G. Taylor for his kind hospitality. Also partial financial support from Kuwait University under grant SP 009, is gratefully acknowledged.