research

Out of equilibrium quantum systems

Out of equilibrium quantum criticality - We have analyzed the out of equilibrium steady state properties of the certain critical impurity models and reported the existence of an effective temperature for certain physical quantities.

Many body Bloch oscillations - We investigated the phenomenon of many body Bloch oscillation in a system of initially trapped hard-core bosons and found that the time evolution can display a plethora of different behaviors depending on the strength of the trap.

Quenches and work distributions - We studied quantum quenches in systems with a fixed number of particles in a large region and reported a new universal behavior at intermediate times, visible in widely different systems.

Expansion dynamics in multichromatic potentials - We studied the non-equilibrium expansion dynamics of hard-core bosons in a one-dimensional lattice subject to a multi-chromatic potential and demonstrated that the extent of partial localization is determined by the single-particle spectrum.

Magnetic and non-magnetic impurities

Local quantum critical systems - We investigated the dynamical properties of the two-channel Anderson model using the non-crossing approximation (NCA) and were able to reproduce the qualitative features of the pseudogap model, including the phase diagram and critical exponents in excellent agreement with the NRG.

STM probing of magnetic impurities - We studied the influence of angular degrees of freedom of magnetic adatoms on metallic surfaces and demonstrated that the spatial dependence of the scanning tunneling spectrum contains sufficient information to infer the orbital degrees of freedom of the magnetic adatom.

Screening cloud - We investigated the impurity screening cloud in the Resonant Level Model and characterized the screening cloud through scaling analyses of impurity-bath correlators and entanglement entropies.

Magnetic Impurities in Spin-Liquids - We studied a magnetic impurity in a two-dimensional U(1) spin-liquid and found a Kondo temperature similar to the one obtained in the presence of Fermi liquid host, corroborating of the remarkable property of this kind of spin-liquids to screen magnetic impurities while being charge insulators.

Superconductivity

Fluctuations in superconducting nano-grains - We studied of the evolution of the superconductor properties of isolated Pb nano-particles as a function of temperature and particle size in single (in collaboration with the experimental group of K. Kern in Stuttgart). We described of the experimental findings with a theoretical model that includes finite size effects and zero temperature. We developed a rigorous treatment for the combined effect of thermal and quantum fluctuations in a zero dimensional superconductor.

Dissipation in a topological Josephson junction - We studied the role of dissipation in a topological superconducting junction and demonstrated that such junction is generically more robust against fluctuations than its non-topological counterpart. As dissipation increases, the phase transition to a superconducting state occurs at a critical value of the dissipation which is four times smaller than that expected for a conventional Josephson junction.

Entanglement content of triplet topological superconductors - We studied the entanglement entropy properties of a two-dimensional p-wave superconductor and analyzed the separate contributions to the entanglement entropy that are proportional to or independent of the perimeter of the system.

Collective Spin Models

Lipkin-Meshkov-Glick model - We pioneered the use of the coherent-spin-state formalism in the study of certain collective spin models arising in Condensed Matter and Nuclear Physics. We derived the exact density of states, eigenstates and observables' properties at the thermodynamic limit and developed a formalism valid for generic

su(2) Hamiltonians.

Mermin model - We applied the spin-coherent states formalism to study Mermin model (central-spin + monochromatic spin bath) and derived the integrated density of states in the thermodynamic limit as well as the characterization of the quantum phase transition.

Spectral properties near exceptional points - We generalized the Bohr-Sommerfeld quantization rules to the spin case both for regular classical orbits and near a separatrix. We developed of a new approach that permits to describe the spectrum in the neighborhood of the critical points.

Quantum Information

Quantum Walks - We proposed a generalized quantum random walk protocol for a particle in a one-dimensional chain using several types of biased quantum coins arranged in periodic and aperiodic sequences. Ballistic, sub-ballistic and diffusive wave-function spreading behaviors were reported.

Adiabatic Quantum Computation - We studied a simplified models for adiabatic quantum computing highlighting the relations between quantum phase transitions and adiabatic quantum computation. We also characterized the state populations dynamics in certain spin systems dynamically driven across quantum phase transition points.

Entanglement Classification - We studied the two- and three-qubit Hilbert space geometries with the help of Hopf fibrations of hyperspheres and demonstrated that the associated Hopf map is strongly sensitive to states' entanglement content. We studied entanglement properties of symmetric states of n qubits with the help of the Majorana representation. Entanglement invariants, either under local unitaries or stochastic local operations and classical communication, were obtained explicitly in terms of the relative positions of the Majorana points.