We consider the consequences of the separation of spin and charge degrees of freedom in 2 + 1 D strongly correlated spin systems. Self-consistent spin and charge motions induced by doping in sites of ground and dual lattices form such a spectrum of quasiparticles which together with the dispersionless character of the collective excitation spectrum and the chemical potential pinning in the band center yield the necessary behavior to support the theory of marginal Fermi liquid formulated by C. M. Varma et al. (Phys. Rev. Lett.63, 1996 (1989)).
We consider the consequences of the separation of spin and charge degrees of freedom in 2 + 1 D strongly correlated spin systems. Self-consistent spin and charge motions induced by doping in sites of ground and dual lattices form such a spectrum of quasiparticles which together with the dispersionless character of the collective excitation spectrum and the chemical potential pinning in the band center yield the necessary behavior to support the theory of marginal Fermi liquid formulated by C. M. Varma et al. (Phys. Rev. Lett.63, 1996 (1989)).
We consider the consequences of separation of spin and charge degrees of freedom in 2+1D strongly correlated spin systems. Self-consistent spin and charge motions induced by doping in sites of ground and dual lattices form such a spectrum of quasiparticles which together with dispersionless character of the collective excitation spectrum and the chemical potential pinning in the band center yield the necessary behavior of charge and spin polarizability to support the theory of marginal liquid formulated by Varma et al. [Phys. Rev. Lett. 63, 1996 (1989)].
We find marginal-Fermi-liquid- (MFL) like behavior in the Hubbard model on a square lattice for a range of hole doping and on-site interaction parameter U. Thereby we use a self-consistent projection operator method. It enables us to compute the momentum and frequency dependence of the single-particle excitations with high resolution. The Fermi surface is found to be holelike in the underdoped regime and electronlike in the overdoped regime. Our calculations concern normal state properties of the system. When a comparison is possible, we find consistency with finite temperature quantum Monte Carlo results. We also find a discontinuous change with doping concentration from a MFL to a Fermi-liquid behavior resulting from a collapse of the lower Hubbard band. This renders Luttinger's theorem inapplicable in the underdoped regime.
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.
Spin–charge separation is considered to be one of the key properties that distinguish low-dimensional electron systems from others. Three-dimensional correlated electron systems are described by the Fermi liquid theory. There, low-energy excitations (quasiparticles) are reminiscent of noninteracting electrons: They carry charges −e and spins 1/2. It is believed that for any one-dimensional correlated electron system, low-lying electron excitations carry either only spin and no charge, or only charge without spin. That is why recent experiments looked for such low-lying collective electron excitations, one of which carries only spin, and the other carries only charge. Here we show that despite the fact that for exactly solvable one-dimensional correlated electron models there exist excitations which carry only spin and only charge, in all these models with short-range interactions the low-energy physics is described by low-lying collective excitations, one of which carries both spin and charge.
The Marginal Fermi Liquid (MFL) hypothesis proposed by Varma et al is derived from a consistent treatment of local spinfluctuations in the Falicov-Kimball model (FKM). Within an infinite-dimensional mean-field approach, a marginal Fermi liquid susceptibility and single-particle self-energy are obtained near half-filling, and a Fermi liquid phase is recovered sufficiently away from half-filling, in agreement with indications from experiments which probe the normal state of the cuprates as a function of doping
In contrast to the well-known Fermi-liquid theory of three dimensions, interacting one-dimensional and quasi-one-dimensional systems of fermions are described at low energy by an effective theory known as Luttinger liquid theory. This theory is expressed in terms of collective many-body excitations that show exotic behavior such as spin-charge separation. Luttinger liquid theory is commonly applied on the premise that ``low energy'' describes both the spin and charge sectors. However, when the interactions in the system are very strong, as they typically are at low particle densities, the ratio of spin to charge energy may become exponentially small. It is then possible at very low temperatures for the single-spin excitation energy to be low compared to the characteristic single excitation charge energy, but still high compared to the characteristic spin energy. This energy window of near ground-state charge degrees of freedom but highly thermally excited spin degrees of freedom is called a spin-incoherent Luttinger liquid. The spin-incoherent Luttinger liquid exhibits a higher degree of universality than the Luttinger liquid and its properties are qualitatively distinct. In this Colloquium some recent theoretical developments in the field are detailed and experimental indications of such a regime in gated semiconductor quantum wires are described.