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.     

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.     

A microscopic model for the coupling of spin fluctuations and charge fluctuation in intermediate valency

A microscopic model is presented to show explicitly how dynamical charge and lattice fluctuations (at zero temperature the zero point motion) will-through spin orbit coupling-induce spin-flip terms off-electrons in intermediate valent and heavy fermion systems. A simple model Hamiltonian coupling charge, lattice, and spin degrees of freedom is derived and diagonalized exactly.     

Quantum dynamics of a driven correlated system coupled to phonons

Nonequilibrium interplay between charge, spin, and lattice degrees of freedom on a square lattice is studied for a single charge carrier doped in the t-J-Holstein model. In the presence of a static electric field we calculate the quasistationary state. With increasing electron-phonon (e-ph) coupling the carrier mobility decreases; however, we find increased steady state current due to e-ph coupling in the regime of negative differential resistance. We explore the distribution of absorbed energy between the spin and the phonon subsystem. For model parameters as relevant for cuprates, the majority of the gained energy flows into the spin subsystem.     

Spinon and <Emphasis Type="Italic">η</Emphasis>-spinon correlation functions of the Hubbard chain

We calculate real-space static correlation functions of spin and charge degrees of freedom of the one-dimensional Hubbard model that are described by operators related to singly occupied sites with spin up or spin down (spinons) and unoccupied or doubly occupied sites (η-spinons). The spatial decay of their correlation functions is determined using density matrix renormalization group results. The nature and spatial extent of the correlations between two sites on the Hubbard chain is studied using the eigenstates and eigenvalues of the two-site reduced density matrix. The results show that the spinon-spinon correlation functions decay algebraically and the η-spinon correlation functions decay exponentially, both in the half-filling and metallic phases. The results provide evidence that these degrees of freedom are organized in boundstates in the interacting system.     

Dual boson approach to collective excitations in correlated fermionic systems

We develop a general theory of a boson decomposition for both local and non-local interactions in lattice fermion models which allows us to describe fermionic degrees of freedom and collective charge and spin excitations on equal footing. An efficient perturbation theory in the interaction of the fermionic and the bosonic degrees of freedom is constructed in the so-called dual variables in the path-integral formalism. This theory takes into account all local correlations of fermions and collective bosonic modes and interpolates between itinerant and localized regimes of electrons in solids. The zero-order approximation of this theory corresponds to an extended dynamical mean-field theory (EDMFT), a regular way to calculate nonlocal corrections to EDMFT is provided. It is shown that dual ladder summation gives a conserving approximation beyond EDMFT. The method is especially suitable for consideration of collective magnetic and charge excitations and allows to calculate their renormalization with respect to “bare” RPA-like characteristics. General expression for the plasmonic dispersion in correlated media is obtained. As an illustration it is shown that effective superexchange interactions in the half-filled Hubbard model can be derived within the dual-ladder approximation.     

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.     

Interplay of charge, spin, orbital and lattice correlations in colossal magnetoresistance manganites

We derive a realistic microscopic model for doped colossal magnetoresistance manganites, which includes the dynamics of charge, spin, orbital and lattice degrees of freedom on a quantum mechanical level. The model respects the SU(2) spin symmetry and the full multiplet structure of the manganese ions within the cubic lattice. Concentrating on the hole doped domain ( 0≤x≤0.5) we study the influence of the electron-lattice interaction on spin and orbital correlations by means of exact diagonalisation techniques. We find that the lattice can cause a considerable suppression of the coupling between spin and orbital degrees of freedom and show how changes in the magnetic correlations are reflected in dynamic phonon correlations. In addition, our calculation gives detailed insights into orbital correlations and demonstrates the possibility of complex orbital states. Received 4 September 2002 / Received in final form 8 November 2002 Published online 31 December 2002     

Exact transformation for spin-charge separation of spin-1/2 fermions without constraints

We demonstrate an exact local transformation which maps a purely Fermionic many-body system to a system of spinful bosons and spinless fermions, demonstrating a possible path to a non-Fermi-liquid state. We apply this to the half-filled Hubbard model and show how the transformation maps the ordinary spin half Fermionic degrees of freedom exactly and without introducing Hilbert space constraints to a chargelike quasicharge fermion and a spinlike quasispin Boson while preserving all the symmetries of the model. We present approximate solutions with localized charge which emerge naturally from the Hubbard model in this form. Our results strongly suggest that charge tends to remain localized for large values of the Hubbard U.     

Spin structures and the nature of the pseudogap in cuprates

The spin and charge structures formed in a Hubbard model for a finite two-dimensional cluster have been studied in the mean field approximation. The self-consistent iterative procedure reduces an uncorrelated initial spin distribution into stable structures with characteristic spectral properties. It has been shown that the density of states of the system for any doping has a sharp minimum at the Fermi level, the pseudogap. This means that the pinning of the gap at the Fermi level is not an exclusive property of a superconducting state, but is also typical of a normal state of spin glasses.     

Zero temperature phase diagram of the ferromagnetic Kondo lattice

We study numerically the one-dimensional ferromagnetic Kondo lattice, a model widely used to describe nickel and manganese perovskites. Due to the competition between double and super-exchange, we find a region where the formation of magnetic islands induces a charge-ordered state. This ordering is present even in the absence of any inter-site Coulomb repulsion and presents an insulating gap associated to the charge structure. We study the metal–insulator transition induced by a magnetic field which removes simultaneously both charge and spin orderings. This new mechanism should be taken into account in theories of charge ordering involving spin degrees of freedom.     

Colossal magnetoresistive manganites

Magnetoelectronic features of the perovskite-type manganites are overviewed in the light of the mechanism of the colossal magnetoresistance (CMR). The essential ingredient of the CMR physics is not only the double-exchange interaction but also other competing interactions, such as ferromagnetic/antiferromagnetic superexchange interactions and charge/orbital ordering instabilities as well as their strong coupling with the lattice deformation. In particular, the orbital degree of freedom of the conduction electrons in the near-degenerate 3d e_g state plays an essential role in producing the unconventional metal–insulator phenomena in the manganites via strong coupling with spin, charge, and lattice degrees of freedom. Insulating or poorly conducting states arise from the long or short-range correlations of charge and orbital, but can be mostly melted or turned into the orbital-disordered conducting state by application of a magnetic field, producing the CMR or the insulator–metal transition.     

Nonequilibrium photo dynamics of low-dimensional strongly correlated electron systems

One of the outstanding contemporary challenges in condensed matter physics is to understand the dynamics of interacting quantum systems exposed to an external perturbation. We theoretically examine nonequilibrium photo dynamics and its interplay of charge, spin, and lattice degrees of freedom on a Hubbard-Holstein chain in one dimension and a t-J-Holstein square lattice in two dimensions. In the chain, performing dynamical density-matrix renormalization group calculations, we find that many phonons generated dynamically after photo irradiation in Mott insulators cause initial relaxation process. On the other hand, in the square lattice with model parameters as relevant for cuprates, a Lanczos-type exact diagonalization calculation shows that the majority of absorbed energy flows into spin subsystem rather than phonon subsystem.     

Effect of charge-spin separation on the conductance through interacting low-dimensional rings

We calculate the conductance through Aharonov-Bohm chain and ladder rings pierced by a magnetic flux which couples with the charge degrees of freedom. The system is weakly coupled to two leads and contains strongly interacting electrons modeled by the prototypical t-J and Hubbard models. For a wide range of parameters we observe characteristic dips in the conductance as a function of magnetic flux which are a signature of spin and charge separation. We also show how the dips evolve when the parameters of the models depart from the ideal case of total spin-charge separation. The ladder ring can be mapped onto an effective model for large anisotropy which can be easily analyzed. These results open the possibility of observing this peculiar many-body phenomenon in anisotropic ladder systems and in real nanoscopic devices.     

3-d Model for strain ordering in steel: I Static effects

We present a spring-defect model in 3-dimensions to describe the connection between elastic distortion and interstitial carbon ordering associated with phase transition from a body centred cubic (BCC) to body centered tetragonal (BCT) structure in BCC metals such as α-iron. The presence or the absence of the carbon is modelled in terms of a pseudo spinŝ=+1or -l.An Ising interaction between carbon atoms is recovered after eliminating the lattice degrees of freedom, which is longranged. The coupling between the spin and lattice degrees of freedom allows for a systematic study of ferroelasticity and the variation of the lattice parameter with carbon concentration. The mean field results for the paraelastic to ferroelastic transition, lattice parameter and static compliance are presented. The significant feature of this calculation is not only a derivation of the defect-defect interaction, but also an explicit calculation of the strain dipole tensor associated with each defect, from a microscopic model.     

Mott transition in the two-dimensional Hubbard model

Spectral properties of the two-dimensional Hubbard model near the Mott transition are investigated by using cluster perturbation theory. The Mott transition is characterized by freezing of the charge degrees of freedom in a single-particle excitation that leads continuously to the magnetic excitation of the Mott insulator. Various anomalous spectral features observed in cuprate high-temperature superconductors are explained in a unified manner as properties near the Mott transition.     

Magnetic and charge orders in zigzag nanographene ribbons

We theoretically study the electronic states in graphene ribbons which are strongly affected by the edge states, the peculiar non-bonding molecular orbitals localized along the zigzag edges of the ribbons. New kinds of edge localized electronic states with spin and charge polarizations are found in the mean field solutions of the extended Hubbard model with onsite and nearest-neighbor Coulomb repulsions. These novel states appear due to the interplay between the edge states and the Fermi instabilities. We also examine the competition between the charge polarized state and the spin polarized state to draw a phase diagram depending on Coulomb parameters. The results obtained by the mean field calculations with the extended Hubbard model modified to include Coulomb integrals provide useful insights to understand and functionalize the nanoscale materials.     

Field-induced antiferromagnetism in the Kondo insulator

The Kondo lattice model, augmented by a Zeeman term, serves as a useful model of a Kondo insulator in an applied magnetic field. A variational mean field analysis of this system on a square lattice, backed up by quantum Monte Carlo calculations, reveals an interesting separation of magnetic field scales. For Zeeman energy comparable to the Kondo energy, the spin gap closes and the system develops transverse staggered magnetic order. The charge gap, however, remains robust up to a higher hybridization energy scale, at which point the canted antiferromagnetism is exponentially suppressed and the system crosses over to a nearly metallic regime. Quantum Monte Carlo simulations support this mean field scenario. An interesting rearrangement of spectral weight with magnetic field is found.