My present interest is focused on strongly correlated systems.
During my Ph.D. I developed from scratch a code to perform Wilson Numerical Renormalization Group (NRG) calculations on quantum impurity models.
We applied this numerical tool to a twofold orbitally degenerate Anderson model with a Hund's coupling with either positive (mimicking usual Hund's rule) or negative coupling (inverted Hund's rule), and we showed that for negative values of the Hund's coupling this model presents a non-Fermi liquid fixed point, similar to the two-impurity Kondo model one, that separates a Kondo-screened regime from a regime in which the impurity forms a singlet on its own. While the two-impurity Kondo model fixed point is unstable under particle-hole symmetry breaking, this fixed point is more robust, since it can only be destabilized by orbital or gauge symmetry breaking.
A characterization of the system via a Fermi liquid like effective Hamiltonian shows a tendency towards a superconducting behavior indicated by the divergence of the bare scattering amplitude in the Cooper channel.
We calculated also the impurity spectral function that allows a deeper insight in the problem. In the Kondo regime close to the fixed point, the DOS displays a very narrow resonance at the Fermi level on top of a broader one. Upon approaching the non-trivial fixed point, this narrow resonance shrinks and finally disappears at the fixed point. Beyond that, we find a gradual opening of a pseudogap within the broader resonance.
The above impurity model is interesting per se, but the most intriguing implications come from the connection between the Mott metal-insulator transition (MIT) and the Anderson impurity model (AIM) physics supported by the Dynamical Mean Field Theory (DMFT).
The main novelty is not in the non-Fermi liquid properties of the model that are shared by many others Kondo models (two-impurity Kondo, two-channel Kondo, pseudogap Kondo), but rather in the fact that the model is an Anderson impurity model and is hence connected to MIT physics.
Close to the MIT the effective Kondo temperature (i.e. the width of the quasiparticle peak) vanishes, hence the system is forced to enter the region around the critical point before MIT occurs. Contrary to the single impurity, the corresponding lattice model has the possibility to develop a bulk order parameter to react against the singular behavior and the Cooper instability is the natural candidate in absence of nesting.
From this point of view the opening of a pseudogap in the single impurity density of states is the fingerprint of a superconducting gap that could be stabilized by the DMFT self-consistency.
The analysis of a three-orbital impurity model with a similar inverted Hund's coupling, performed using together NRG and Conformal Field Theory, shows an even richer phase diagram. In the Conformal Field Theory description of the model a central role is played by a discrete Z3 symmetry, reflecting the orbital permutational symmetry. In this case we find that in the presence of particle-hole symmetry there is a quantum critical point separating a Fermi liquid phase from a stable non-Fermi liquid one. While the stable non-Fermi liquid phase does not survive particle-hole symmetry breaking and is replaced by a Fermi liquid, the unstable critical point survives upon doping and presents once more superconducting diverging susceptibilities. We pointed out the relevance of this model as a possible interpretation for the behavior of single molecule transistors based on C60n- molecules. The relation between the non-Fermi liquid stable phase at particle-hole symmetry and the non-Fermi liquid phase found by Ingersent, Ludwig and Affleck (cond-mat/0505303) in their study of a trimer of Kondo impurities offers further motivations of interest in this model.
In a work in preparation, we studied the case of an impurity formed by a plaquette of spins with an antiferromagnetic coupling between nearest neighbors. Using conformal field theory and NRG we obtained a solution for the fixed points of this model, finding that the competition between Kondo screening and RKKY couplings generates an unstable fixed point. The relevant operators close to the critical point include all the instabilities which are believed to be relevant in the case of cuprates: antiferromagnetic ordering, flux-phases, d-wave superconductivity, etc. In the optic of a cluster-DMFT treatment of the Hubbard model using a plaquette as the impurity, the relevance of this solution is crucial to clarify the presence of a quantum critical point influencing the physics of the model.
At the moment I'm pursuing the project of setting up the DMFT self-consistency using NRG as the impurity solver. The possibility to treat multi-orbital models allows to extend the range of applications to cluster-DMFT, where spatial correlations can be taken into account, and offers the possibility to understand if the non-Fermi liquid behavior of some impurity models is relevant for lattice systems. In this context I'm also gaining some expertise with an exact diagonalization code applied to cluster DMFT.
On the computational side my main interest is in further developing NRG. The NRG technique is a powerful and flexible tool that can be applied to a large variety of problems, ranging from quantum dots to strongly correlated lattice systems through the implementation of DMFT self-consistency.
From the point of view of analytical techniques I'm familiar with bosonization and conformal field theory. In particular the latter is somehow a natural counterpart of NRG and proves extremely useful and versatile when the complexity of the impurity grows beyond the limits of numerical techniques.
For the degree and the master degree we studied some properties of the t-J model using non-abelian U(1)xSU(2) Chern-Simons bosonization as a possible starting point to describe the pseudogap phase of underdoped cuprates. This approach is based on a formal decomposition of electronic degrees of freedom into spin and charge ones.
The system resulting from a suitable mean field approximation contains spinons and holons coupled to an abelian gauge field. The spinons are massive due to the presence of antiferromagnetic background distortions induced by holons, while the gauge field exhibits a Reitzer singularity due to the interaction with finite density holons.
The interplay between gauge field dissipation and the spinon mass term determines for instance the crossover between metallic and insulating behavior in the in-plane resistivity.
We obtained an analytic expression for the electron Green's function
and for the electron lifetime that indicates a composite nature of the
electron due to the attraction between holons and spinons mediated by
the gauge field, hence supporting neither a true spin-charge separation nor a
confinement picture, but rather some kind of intermediate situation.