P. A. Marchetti

Duality-invariant quantum field theories of charges and monopoles

We present a manifestly Lorentz– and SO(2)–Duality–invariant local Quantum Field Theory of electric charges, Dirac magnetic monopoles and dyons. The manifest invariances are achieved by means of the PST–mechanism. The dynamics for classical point particles is described by an action functional living on a circle, if the Dirac–Schwinger quantization condition for electric and magnetic charges holds. The inconsistent classical Field Theory depends on an arbitrary, but fixed, external vector field, a generalization of the Dirac–string. Nevertheless, the Quantum Field Theory, obtained from this classical action via a functional integral approach, turns out to be independent of the particular vector field chosen, and thus consistent, if the Dirac–Schwinger quantization condition holds. We provide explicit expressions for the generating functionals of observables, proving that they are Dirac–string independent. Since Lorentz–invariance is manifest at each step, the quantum theory admits also a manifestly diffeomorphism invariant coupling to external gravity. Relations with previous formulations, and with SO(2)–non invariant theories are clarified.

Dimensional reduction of U(1) × SU(2) Chern-Simons bosonization: Application to the t-J model

Abstract We perform a dimensional reduction of the U (1) × SU (2) Chern-Simons bosonization and we apply it to the t - J model, relevant model for high T c superconductors. This procedure yields a decomposition of the electron field into the product of two “semionic” fields, i.e. fields obeying abelian braid statistics with statistics parameter θ = 1 4 , one carrying the charge and the other the spin degrees of freedom. A mean-field theory is then shown to reproduce correctly the large-distance behaviour of the correlation functions of the 1D t - J model at t ⪢ J . This results shows that to capture the essential physical properties of the model one needs a specific “semionic” form of spin-charge separation.

Gauge field theory of transport and magnetic relaxation in underdoped cuprates

An interpretation of the transport and magnetic relaxation properties of underdoped cuprates based on the recently proposed U(1) x SU(2) Chern-Simons gauge field theory is proposed, which rakes into account the short-range antiferromagnetic order. The interplay of the doping dependent spin-gap (explicitly derived by us) effect and dissipation due to gauge fluctuations gives rise to a crossover from metallic to insulating behaviour of the conductivity as temperature decreases, in semi-quantitative agreement with experimental data. For the same reason the magnetic relaxation rate shows a maximum nearby. Various crossover temperatures related to spin-gap effects are shown to be different manifestations of the same energy scale.

In-plane conductivity anisotropy in the underdoped cuprates using the spin-charge gauge approach

Applying the recently developed spin-charge gauge theory for the pseudogap phase in cuprates, we propose a self-consistent explanation of several peculiar features of the far-infrared in-plane ac conductivity, including a broad peak as a function of frequency and significant anisotropy at low temperatures, along with a similar temperature-dependent in-plane anisotropy of dc conductivity in lightly doped cuprates. The anisotropy of the metal-insulator crossover scale is considered to be responsible for these phenomena. The obtained results are in good agreement with experiments. An explicit proposal is made to further check the theory.

U(1)×SU(2) Gauge Theory of Underdoped Cuprate Superconductors

The U(1) x SU(2) Chern-Simons gauge theory is applied to study the 2D t-J model describing the normal state of underdoped cuprate superconductors. The U(1) field produces a flux phase for holons converting them into Dirac-like fermions, while the SU(2) field, due to the coupling to holons gives rise to a gap for spinons. An effective low-energy action involving holons, spinons and a self-generated U(1) gauge field is derived. The Fermi surface and electron spectral function obtained are consistent with photoemission experiments. The theory predicts a minimal gap proportional to doping concentration. It also explains anomalous transport properties.

Hall effect, edge states and Haldane exclusion statistics in two-dimensional space

We clarify the relation between two kinds of statistics for particle excitations in planar systems: the braid statistics of anyons and the Haldane exclusion statistics(HES). It is shown non-perturbatively that the HES exists for incompressible anyon liquid in the presence of a Hall response. We also study the statistical properties of a specific quantum anomalous Hall model with Chern-Simons term by perturbation in both compressible and incompressible regimes, where the crucial role of edge states to the HES is shown.

U(1) × SU(2) gauge field theory of transport and magnetic relaxation in underdoped High Tc cuprates

Based on recently proposed U(1) × SU(2) Chern-Simons gauge field theory, an interpretation of the transport and magnetic relaxation properties of underdoped cuprates is proposed. The interplay of the doping-dependent spin gap effect and dissipation due to gauge fluctuations gives rise to a crossover from metallic to insulating behavior of conductivity as temperature decreases, in semi-quantitative agreement with experimental data. For the same reason the magnetic relaxation rate shows a maximum nearby.