We investigate a microscopic model for strongly correlated electrons with both on-site and nearest-neighbor Coulomb repulsion on a two-dimensional (2D) square lattice. This exhibits a state in which electrons undergo a ``somersault'' in their internal spin space (spin flux) as they traverse a closed loop in external coordinate space. When this spin-$\frac{1}{2}$ antiferromagnetic (AFM) insulator is doped, the ground state is a liquid of charged, bosonic meron vortices, which for topological reasons are created in vortex-antivortex pairs. The magnetic exchange energy of the distorted AFM background leads to a logarithmic vortex-antivortex attraction which overcomes the direct Coulomb repulsion between holes localized on the vortex cores. This leads to the appearance of preformed charged pairs. We use the configuration interaction (CI) method to study the quantum translational and rotational motion of various charged magnetic solitons and soliton pairs. The CI method systematically describes fluctuation and quantum tunneling corrections to the Hartree-Fock approximation. We find that the lowest-energy charged meron-antimeron pairs exhibit d-wave rotational symmetry, consistent with the symmetry of the cuprate superconducting order parameter. For a single hole in the 2D AFM plane, we find a precursor to spin-charge separation in which a conventional charged spin polaron dissociates into a singly charged meron-antimeron bound pair. This model provides a unified microscopic basis for (i) non-Fermi-liquid transport properties, (ii) d-wave preformed charged carrier pairs, (iii) midinfrared optical absorption, (iv) destruction of AFM long-range order with doping and other magnetic properties, and (v) certain aspects of angle-resolved photoemission spectroscopy.
We investigate a microscopic model for strongly correlated electrons with both on-site and nearest-neighbor Coulomb repulsion on a two-dimensional (2D) square lattice. This exhibits a state in which electrons undergo a ``somersault'' in their internal spin space (spin flux) as they traverse a closed loop in external coordinate space. When this spin-21 antiferromagnetic (AFM) insulator is doped, the ground state is a liquid of charged, bosonic meron vortices, which for topological reasons are created in vortex-antivortex pairs. The magnetic exchange energy of the distorted AFM background leads to a logarithmic vortex-antivortex attraction which overcomes the direct Coulomb repulsion between holes localized on the vortex cores. This leads to the appearance of preformed charged pairs. We use the configuration interaction (CI) method to study the quantum translational and rotational motion of various charged magnetic solitons and soliton pairs. The CI method systematically describes fluctuation and quantum tunneling corrections to the Hartree-Fock approximation. We find that the lowest-energy charged meron-antimeron pairs exhibit d-wave rotational symmetry, consistent with the symmetry of the cuprate superconducting order parameter. For a single hole in the 2D AFM plane, we find a precursor to spin-charge separation in which a conventional charged spin polaron dissociates into a singly charged meron-antimeron bound pair. This model provides a unified microscopic basis for (i) non-Fermi-liquid transport properties, (ii) d-wave preformed charged carrier pairs, (iii) midinfrared optical absorption, (iv) destruction of AFM long-range order with doping and other magnetic properties, and (v) certain aspects of angle-resolved photoemission spectroscopy.
This thesis examines the properties of a new microscopic model for non-Fermi-liquid behavior and d-wave pairing in a strongly correlated quasi-two-dimensional (2D) electron gas with purely repulsive interactions. Themicroscopic Hamiltonian for this system involves a nearest neighbor electron hopping matrix element t, an on-site Coulom b repulsion U , and a nearest neighbor Coulomb repulsion V. We suggest that nearest neighbor Coulomb repulsion on the energy scale of t stabilizes a state in which electrons undergo a �somersault� in their internal spin-space (spin-flux). Spin-flux is a new form of spontaneous symmetry breaking in a strongly correlated electron system in which the Hamiltonian acquires a term with the symmetry of spin-orbit coupling at the mean-field level. Spin-flux modifies the single quasi-particle dispersion relations from that of a conventional antiferro-magnet (AFM ). When this spin-1/2 A FM insulator is doped, the charge carriers are mobile, charged, bosonic meron-vortex solitons accompanied by unoccupied states deep inside the Mott-Hubbard charge-transfer gap. This model provides a unified microscopic basis for (i) non-Fermi-liquid transport properties for low and intermediate doping, (ii) mid-infrared optical absorption, (iii) destruction of A FM long range order with doping, (iv) angled resolved spectroscopy (ARPES), (v) d-wave preformed charge carrier pairs, an d (vi) a transition from the non-Fermi liquid state to a conventional Fermi-liquid metal for large doping. The approximations used to study the 2D spin-flux Hubbard model are the unrestricted Hartree-Fock Approximation and the Configuration Interaction (C l) Method. In ID, the C l approximation leads to excellent agreement with the exact Bethe Ansatz solution of the Hubbard model, as well as a clear demonstration of the spin-charge separation: the charge of the doping hole is carried by charged bosonic domain-walls, while the spin of the doping hole is carried by neutral fermionic domain-walls. In 2D, the C l method suggests a precursor to the spin-charge separation: addition of a single hole leads to the appearance of a charge-carrying vortex (the meron-vortex) bound to a spin-carrying antivortex.
We demonstrate from first principles that when a charge carrier is added to a $\mathrm{spin}\ensuremath{-}1/2$ antiferromagnetic Mott insulator in either a one- or two-dimensional lattice, the self-consistent, Hartree-Fock ground state consists of a magnetic soliton texture with a doubly degenerate electronic level at the center of the Mott-Hubbard charge gap. This model is appropriate to systems with weak interchain or interlayer magnetic couplings in which long-range antiferromagnetic order is observed in the absence of charge carriers (doping). These magnetic solitons mediate the destruction of the magnetic order as the charge carrier concentration is increased. In a one-dimensional lattice with nearest-neighbor hopping t, on-site Coulomb repulsion U, and self-consistent, antiferromagnetic moment amplitude S, we find that a charged, fermionic, magnetic domain wall soliton with a weakly ferromagnetic core, centered between two sites, has lower Hartree-Fock energy than a corresponding charged quasiparticle in one of the Mott-Hubbard bands. However, for US/t>2, this soliton is unstable to the formation of a lower energy charged, bosonic domain wall soliton, centered on a single site. For US/t<2, both of the above solitons are charged bosons. The self-consistent structure of these solitons exhibits no rotation of the local magnetic moments, but only a local suppression of the local moment amplitude in the vicinity of the hole. In the absence of doping, charge neutral domain wall solitons exhibit spin rotation within their core region. The equilibrium core size $\ensuremath{\rho}$ is determined by the degree of magnetic anisotropy. The ferromagnetic core soliton exhibits a pair of nondegenerate near-midgap electronic states. The antiferromagnetic core soliton exhibits a pair of nondegenerate electronic states that are symmetric about the midgap energy and that merge into the continuum as the anisotropy effects are made small and the soliton core radius $\ensuremath{\rho}$ becomes very large. The two-dimensional antiferromagnetic Mott insulator exhibits analogous behavior to the one-dimensional model. This analogy is precise for a 2D antiferromagnet exhibiting spin flux. For the undoped Mott insulator, the ferromagnetic core meron vortex (``lotus flower'' configuration of local magnetic moments) exhibits a doubly degenerate electronic midgap state in the continuum model and is the analog of the 1D neutral domain wall soliton. We demonstrate that a hole added to the 2D system can form a charged bosonic collective excitation, in which the spin background around the hole forms a planar vortex with local antiferromagnetic correlations at infinity and vanishing local-moment amplitude at the core of the soliton.
One of the central issues in the study of high-temperature superconducting cuprates which are composed of two-dimensional (2D) CuO 2 planes is whether the 2D systems with strong electron correlation behave as a Fermi liquid or a non-Fermi-liquid-like one-dimensional (1D) system with electron correlation. In this article, we start with the detailed examination of the electronic structure in cuprates and study theoretically the spin and charge dynamics in 1D and 2D cuprates. The theoretical background of spin-charge separation in the 1D model systems including the Hubbard and t - J models is presented. The first direct observation of collective modes of spin and charge excitations in a 1D cuprate, which are called spinons and holons respectively, in angle-resolved photoemission spectroscopy (ARPES) experiments is reviewed in the light of the theoretical results based on the numerically exact-diagonalization method. The charge and spin dynamics in 1D insulating cuprates is also discussed in connection with the spin-charge separation. The arguments are extended to the 2D cuprates, and the unique aspects of the electronic properties of high-temperature superconductors are discussed. Special emphasis is placed on the d-wave-like excitations in insulating 2D cuprates observed in ARPES experiments. We explain how the excitations are caused by the spin-charge separation. The charge stripes observed in the underdoped cuprates are examined in connection with spin-charge separation in real space.
A real spin-charge separation scheme is found based on a saddle-point state of the t-J model. In the one-dimensional (1D) case, such a saddle-point reproduces the correct asymptotic correlations at the strong-coupling fixed point of the model. In the two-dimensional (2D) case, the transverse gauge field confining spinon and holon is shown to be gapped at finite doping so that a spin-charge deconfinement is obtained for its first time in 2D. The gap in the gauge fluctuation disappears at half-filling limit, where a long-range antiferromagnetic order is recovered at zero temperature and spinons become confined. The most interesting features of spin dynamics and transport are exhibited at finite doping where exotic residual couplings between spin and charge degrees of freedom lead to systematic anomalies with regard to a Fermi-liquid system. In spin dynamics, a commensurate antiferromagnetic fluctuation with a small, doping-dependent energy scale is found, which is characterized in momentum space by a Gaussian peak at (\ensuremath{\pi}/a,\ensuremath{\pi}/a) with a doping-dependent width (\ensuremath{\propto} \ensuremath{\surd}\ensuremath{\delta} , \ensuremath{\delta} is the doping concentration). This commensurate magnetic fluctuation contributes a non-Korringa behavior for the NMR spin-lattice relaxation rate. There also exists a characteristic temperature scale below thich a pseudogap behavior appears in the spin dynamics. Furthermore, an incommensurate magnetic fluctuation is also obtained at a finite energy regime. In the transport, a strong-range phase intereference leads to an effective holon Lagrangian which can give rise to a series of interesting phenomena including linear-T resistivity and a T2 Hall angle. We discuss the striking similarities of these theoretical features with those found in the high-Tc cuprates and give a consistent picture for the latter. Electronic properties like Fermi surface and superconducting pairing in this framework are also discussed.
We demonstrate that the configuration interaction (CI) approximation recaptures essential features of the exact (Bethe-ansatz) solution to the one-dimensional (1D) Hubbard model. As such, it provides a valuable route for describing effects that go beyond mean-field theory for strongly correlated electron systems in higher dimensions. The CI method systematically describes fluctuation and quantum tunneling corrections to the Hartree-Fock approximation (HFA). HFA predicts that doping a half-filled Hubbard chain leads to the appearance of charged spin polarons or charged domain-wall solitons in the antiferromagnetic background. The CI method, on the other hand, describes the quantum dynamics of these charged magnetic solitons and quantum tunneling effects between various mean-field configurations. In this paper, we test the accuracy of the CI method against the exact solution of the one-dimensional Hubbard model. We find remarkable agreement between the energy of the mobile charged bosonic domain wall (as given by the CI method) and the exact energy of the doping hole (as given by the Bethe ansatz) for the entire U/t range. The CI method also leads to a clear demonstration of the spin-charge separation in one dimension. Addition of one doping hole to the half-filled antiferromagnetic chain results in the appearance of two different carriers: a charged bosonic domain wall (which carries the charge but no spin) and a neutral spin-1/2 domain wall (which carries the spin but no charge).
The Fermi liquid theory is a central concept in modern condensed matter physics used to describe conventional metals. A state of this universality class consists of well-defined quasiparticles, which occupy a finite number of states within a Fermi volume defined in momentum space. According to the Luttinger’s theorem, such a state encloses a Fermi volume proportional to the electron density modulo the filled bands if no symmetry is broken. In the past decades strong deviations from Fermi liquid theory have been observed in the scaling behavior of thermodynamic observables in different materials, among which are for instance cuprates and iron pnictides. This thesis is about two prototypical systems that can not be described by Fermi liquid theory. The first part of this work investigates two-dimensional effective models, which are in a Mott insulating state at half-filling and have a finite conductivity when doped with holes. In such a Mott insulating state, the charge carriers are strongly localized due to the Coulomb repulsion. Hence, strong correlations are assumed to have a strong impact on the formation of the ground state, also in the regime of small hole concentration. In a first project we have used a so-called spinon dopon mean-field theory to represent the two-dimensional Fermi-Hubbard model with strong on-site repulsive interaction in effective degrees of freedom, in which the holes can be embedded into a quantum spin liquid. The corresponding SU(2) invariant ground state belongs to the class of fractionalized Fermi liquids. In a second project we investigate a quantum dimer model, an effective model based on a Hilbert space spanned by short range singlets and bound states of holes and spins. The focus here is on the calculation of the hole-part of the electron spectral function by using exact diagonalization and its comparison with two analytic methods, a diagrammatic computation based on the Bethe-Salpeter equation and a so-called two-mode approximation. The electron spectral function shows a similar analytic form in momentum space between nodal and antinodal point when compared to results from photoemission spectroscopy experiments on cuprates. Furthermore, in a subsequent work we calculate the exact ground state of the quantum dimer model along a certain parameter line. In order to analyze the behavior of the elctron spectral function when increasing the density of holes, we investigate the Fermi-Hubbard model in a current project using a dynamical mean-field approach. To solve the 4-site cluster impurity problem, we use a numerical renormalization group approach. However, numerical limitations force us to restrict the analysis to spin-polarized baths. According to the spectral data, the system is similar to the SU(2) invariant case at half-filling in a Mott insulating state and posseses a momentum-selective energy gap at finite doping. The topology of the Fermi surface shows a Lifshitz transition when increasing the hole concentration. Here, the curvature of the Fermi surface changes from electron- to hole-like. For comparison we apply the dynamical mean-field theory also to the quantum dimer model and observe that the electron spectral functions at finite doping are qualitatively similar to that of the two-dimensional Fermi-Hubbard model. The second half of the work is about Tomonaga-Luttinger liquid theory, which is used to describe the low-energy effective degrees of freedom of one-dimensional systems. Here, we first discuss a conceptional extension of the operator-based bosonization theory for one-dimensional systems. This extension is especially suited for inhomogeneous one-dimensional systems. First, we investigate a one-dimensional system with a local interation potential and compute an exact solution of the single particle propagator at T = 0. The critical exponent of the single particle propagator has an unconventional form as a function of the microscopic Tomonaga-Luttinger parameters, which is not covered by the original Luttinger paradigm postulated by F. Duncan M. Haldane. In a second project on one-dimensional systems, we study the impact of scattering processes among bosonic low-energy excitations on the thermalization process. Such scattering processes are irrelevant on large length scales, however strongly affect the dynamics. In our analytic analysis we focus on a experimental setup, where a one-dimensional Bose gas is instantaneously splitted in two identical, however strongly correlated, halves of one-dimensional electronic systems. In the following, the corresponding non-equilibrium state runs through multiple regimes in time, such as a metastable prethermalization regime. However, above a certain threshold in time such scattering processes cause an effective thermalization of the system. In order to demonstrate this, we compute the kinetic equation in the Keldysh field integral formalism from a diagrammatic expansion based on a self-consistent Born approximation.