Thermodynamic, magnetic and transport properties of strongly correlated systems

Abstract

Recently, there has been increasing interested in studying several properties of strongly correlated systems. The presence of frustration, for instance, can affect the magnetism of the system due to the high degeneracy of the ground state. Systems with specific geometries can be designed through vacancy engineering, obtaining systems with a more intense magnetic response for a given regime of interactions. It is also possible to study the effect of time-dependent perturbations to obtain different properties. It is relevant to note that the quantum properties of interacting systems can be perceived at finite temperatures, allowing the analysis of entanglement effects in this situation. In this thesis we study the Hubbard Hamiltonian through numerical simulations, specifically through determinant quantum Monte Carlo, with the aim of understanding the effects of electronic interaction on magnetic correlations and transport properties. We firstly analyze the kagome lattice, which is known to have frustration. We find a transition between a paramagnetic metal and a Mott insulator at U/t = 6.5 } 0.5, and find that it is possible to adiabatically cool our system to entropies smaller than s ≈ ln 2. We then investigate the entanglement between a site with the rest of the lattice at finite temperatures as a means to signal Mott transitions. To do this, we study the Hubbard Hamiltonian in three different two-dimensional geometries whose Mott transitions are known and analyze the relation between the single-site entanglement with the Hubbard interaction and with the electronic density. We find that the entanglement and its derivatives with respect to U and with respect to n allow us to reasonably estimate the Mott transition. Another topic addressed was the study of a nodal line semimetal, created through vacancy engineering from a honeycomb network. We identified that this system becomes a magnetic insulator for any U/t > 0, and has inhomogeneous magnetism within the unit cell, different from the pristine network. Finally, we investigated how to use photoirradiation to enhance superconductivity in a bilayer. We observed that it is possible to introduce a vector potential in the bilayer Hubbard and t-J models that can be fine-tuned to leave the ground state and access a state with a higher superconducting response.