The spin-rotationally invariant SU(2) approach to the Hubbard model is extended to accommodate the charge degrees of freedom.Both U(1) and SU(2) gauge transformation are used to factorize the charge and spin contribution to the original electron operator in terms of the emergent gauge fields.It is shown that these fields play a similar role as phonons in the BCS theory: they provide the "glue" for fermion pairing.By tracing out gauge bosons the form of paired states is established and the role of antiferromagnetic correlations is explicated.
Superconductivity in the strongly correlated electronic systems described by the Hubbard model for slightly less than half-filled band is shown to arise from the condensation of charge + e holons which are bosons. The holon effective mass is found to be very close to that of the band electrons and they have a strong nearest neighbour repulsion induced by the spin fluctuations. They interact with an U(1) part of the collective SU(2) gauge field (named S-gauge field) of the spin system. This results in spontaneous symmetry breaking of the holon field and the appearance of the Anderson-Higgs phenomenon. The interesting possibility of the SU(2) gauge field-spinon coupled system retaining some gapless excitation spectrum inspite of the spontaneous symmetry breaking in the holon field is pointed out.
This thesis deals with different aspects of high temperature superconductivity in hole-doped cuprates. We assume the t - J model to describe the CuO2 planes of cuprates and we use a spin-charge gauge approach with spin-charge separation to describe holes in terms of a spinless fermion carrying the charge (holon) and a neutral boson carrying spin 1/2 (spinon), coupled by a slave-particle gauge field. In this framework we consider the effects of the presence of a finite density of incoherent holon pairs in the normal state as a precursor of superconductivity. We show that it is possible to take such pairs into account through a strongly direction dependent spectral weight for holons, which suppresses quasi-particles starting from the anti-nodal directions, and a wave function renormalization for the slave particle gauge field. In this way we prove that, when temperature is reduced, the formation of holon pairs causes both the deviation from linearity of the resistivity and the deviation from the constant value of the Knight shift. Moreover we point out the need for a negative next-nearest-neighbor hopping term ((t - t' - J model) to get a good continuum limit and to evaluate the Knight shift. These results are obtained through a Green's function, which follows naturally from the formalism and analytically interpolates between a Fermi liquid-like behavior and a d-wave superconductor when the coherence length of the holon pair order parameter is increased. The system preserves a finite Fermi surface until the superconducting transition, where it reduces to four nodes. Finally when, at lower temperatures, both the holon pairs and the RVB spinon pairs condense we enter the superconducting phase. In this phase we study the magnetic excitations showing how to extend to spin waves the hourglass-shape dispersion, found for spinons near the antiferromagnetic vector, if a suitable local mechanism of attraction between spinon and anti-spinon is assumed. The resulting spin wave Green's function, whose imaginary part is directly comparable with experiments, generates the hourglass with a finite gap between the two branches. Since the U(1) slave-particle gauge field gains mass in the superconducting phase via Anderson-Higgs mechanism, we propose the necessary mechanism of attraction comes from the unbroken Z2 subgroup of the U(1) gauge group.
By means of the functional-integral formulation we discuss the occurrence of superconductivity resulting from Bose-Einstein condensation within a model describing preformed pairs which coexist in thermal equilibrium with unpaired fermions. At saddle-point level we study the thermodynamic properties of the model as functions of the boson excitation energy $\ensuremath{\nu},$ discussing the results in connection with the phenomenology of the pseudogap state of the superconducting cuprates. For temperatures above the Bose-Einstein condensation temperature
Tc we also analyze the effects of Gaussian fluctuations on the critical temperature and on the boson spectrum. Finally, we compare the bosonic effective action which controls thermal fluctuations of the mixture to the time-dependent Ginzburg-Landau functional of an interacting fermionic system at intermediate coupling.
We implement the rotationally invariant formulation of the two-dimensional Hubbard model, with nearest-neighbors hopping
t, which allows for the analytical study of the system in the low-energy limit. Both U(1) and SU(2) gauge transformations are used to factorize the charge and spin contributions to the original electron operator in terms of the corresponding gauge fields. The Hubbard Coulomb energy
U term is then expressed in terms of quantum phase variables conjugate to the local charge and variable spin-quantization axis, providing a useful representation of strongly correlated systems. It is shown that these gauge fields play a similar role as phonons in the BCS theory: they act as the ``glue'' for fermion pairing. By tracing out gauge degrees of freedom, the form of paired states is established and the strength of the pairing potential is determined. It is found that the attractive pairing potential in the effective low-energy fermionic action is nonzero in a rather narrow range of
U/t.
We study the slave-boson $t\ensuremath{-}J$ model of cuprates with high superconducting transition temperatures, and derive its low-energy effective field theory for the charge-spin separated state in a self-consistent manner. The phase degrees of freedom of the mean field for hoppings of holons and spinons can be regarded as a U(1) gauge field,
Ai. The charge-spin separation occurs below a certain temperature,
TCSS, as a deconfinement phenomenon of the dynamics of
Ai. Below a certain temperature
TSG(<TCSS), the spin-gap phase develops as the Higgs phase of the gauge-field dynamics, and
Ai acquires a mass
mA. The effective field theory near
TSG takes the form of a Ginzburg-Landau theory of a complex scalar field $\ensuremath{\lambda}$ coupled with
Ai, where $\ensuremath{\lambda}$ represents d-wave pairings of spinons. Three dimensionality of the system is crucial to realize a phase transition at
TSG. By using this field theory, we calculate the dc resistivity $\ensuremath{\rho}.$ At
T>TSG, $\ensuremath{\rho}$ is proportional to T. At
T<TSG, it deviates downward from the T-linear behavior as $\ensuremath{\rho}\ensuremath{\propto}T{1\ensuremath{-}{c(T}_{\mathrm{SG}}\ensuremath{-}{T)}^{d}}.$ When the system is near (but not) two dimensional, due to the compactness of the phase of the field $\ensuremath{\lambda},$ the exponent d deviates from its mean-field value
1/2 and becomes a nonuniversal quantity which depends on temperature and doping. This significantly improves the comparison with the experimental data.