of the thesisWe consider the theory of high temperature superconductivity from the viewpoint of a strongly correlated electron system. In particular, we discuss Gutzwiller projected wave functions, which incorporate strong correlations by prohibiting double occupancy in orbitals with strong on-site repulsion. After a general overview on high temperature superconductivity, we discuss Anderson's resonating valence bond (RVB) picture and its implementation by renormalized mean field theory (RMFT) and variational Monte Carlo (VMC) techniques. In the following, we present a detailed review on RMFT and VMC results with emphasis on our recent contributions. Especially, we are interested in spectral features of Gutzwiller-Bogoliubov quasiparticles obtained by extending VMC and RMFT techniques to excited states. We explicitly illustrate this method to determine the quasiparticle weight and provide a comparison with angle resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM). We conclude by summarizing recent successes and by discussing open questions, which must be solved for a thorough understanding of high temperature superconductivity by Gutzwiller projected wave functions.

We present a Ginzburg-Landau formulation of the bosonic resonating-valence-bond ͑RVB͒ theory of superconductivity. The superconducting order parameter is characterized by phase vortices that describe spinon excitations and the transition to the superconducting state occurs when such phase vortices ͑un͒bind. We show that the boson RVB theory always leads to hc/2e flux quanta and that the presence of a trapped spin-1/2 moment inside a vortex core gives rise to observable consequences for the low-temperature field-dependent specific heat. We also show that the cores of magnetic fluxoids exhibit enhanced antiferromagnetic correlations with a midgap energy scale and discuss some experimental implications.

We present a variational Monte Carlo (VMC) study of spontaneous Fermi surface symmetry breaking in the t − J model. We find that the variational energy of a Gutzwiller projected Fermi sea is lowered by allowing for a finite asymmetry between the x-and the y-directions. However, the best variational state remains a pure superconducting state with d-wave symmetry, as long as the underlying lattice is isotropic. Our VMC results are in good overall agreement with slave boson mean field theory (SBMFT) and renormalized mean field theory (RMFT), although apparent discrepancies do show up in the half-filled limit, revealing some limitations of mean field theories. VMC and complementary RMFT calculations also confirm the SBMFT predictions that many-body interactions can enhance any anisotropy in the underlying crystal lattice. Thus, our results may be of consequence for the description of strongly correlated superconductors with an anisotropic lattice structure.

We investigate the excitation spectrum of a two-dimensional resonating valence bond (RVB) state. Treating the pi-flux phase with antiferromagnetic correlations as a variational ground state, we recover the long wavelength magnon as an "RVB exciton." However, this excitation does not exhaust the entire spectral weight and the high-energy spectrum is dominated by fermionic excitations. The latter can be observed directly by inelastic neutron scattering, and we predict their characteristic energy scales along different high symmetry directions in the magnetic Brillouin zone. We also interpret experimental results on two magnon Raman scattering and midinfrared absorption within this scenario.

We present experimental data for the Raman intensity in the spin-Peierls compound CuGeO3 and theoretical calculations from a one-dimensional frustrated spin model. The theory is based on (a) exact diagonalization and (b) a recently developed solitonic mean field theory. We find good agreement between the 1D-theory in the homogeneous phase and evidence for a novel dimerization of the Raman operator in the spin-Peierls state. Finally we present evidence for a coupling between the interchain exchange, the spin-Peierls order parameter and the magnetic excitations along the chains. 78.20.Ls Low-dimensional spin systems exhibit many unusual properties resulting from quantum and dimensionality effects. An example is the continuum of spin-wave excitations in quantum one-dimensional (1D) spin systems which has been predicted for a long time [1] and has recently been confirmed by neutron scattering experiments [2] on KCuF 3 .Quantum 1D spin systems also show a variety of instabilities. Of particular interest is the spin-Peierls (SP) phase due to residual magnetoelastic couplings [3], which leads to the opening of a gap in the spin excitation spectrum. The discovery [4] of the spin-Peierls transition below T SP = 14 K in an inorganic compound, CuGeO 3 , has attracted widespread attention. This compound consists of chains of spin-1/2 Cu 2+ ions coupled by antiferromagnetic superexchange via the oxygen orbitals [4,5]. The Cu ions lie along the crystallographic c-axis and the exchange along the chains can be modeled by the 1D Hamiltonianwhere δ is the dimerization parameter that vanishes above T SP [6,7]. The special geometry [6,8] of the superexchange path in CuGeO 3 leads to a small value of the exchange integral J ≈ 150K and a substantial n.n.n. frustration term ∼ α which competes with the n.n. antiferromagnetic exchange. The interchain couplings have been estimated to be small, J b ≈ 0.1J and J a ≈ −0.01J for the interchain exchange constants along a-and b-directions, respectively [5]. The phase diagram of H in Eq.(1) has been calculated using the density-matrix renormalization-group method [9]. For δ = 0 and α < α c ≈ 0.2411, the ground state is gapless and renormalizes to the Heisenberg fixed point. For α = 0.5 and δ = 0, the ground state is given by a valence-bond state and a gap of order J/2 induced by frustration is present. While the evaluation of the dynamical properties of (1) is a challenge to theory, the rich phase diagram can be explored by a variety of interesting experiments. In this context, the substantial value of the n.n.n. exchange integral in CuGeO 3 allows the experimental investigation of the effects of competing interactions in a low dimensional magnet, both in the uniform and in the spin-Peierls state.An experimental method particularly suited for the study of magnetic excitations in an antiferromagnet is two magnon Raman scattering. For CuGeO 3 , the Raman operator in A 1g symmetry [10]is proportional toIn the homogeneous state (δ = γ = 0) the interaction Hamiltonian commutes with the Heisenberg...