Entanglement of a 3D generalization of the Kitaev model on the diamond lattice

We study the entanglement properties of a three dimensional generalization of the Kitaev honeycomb model proposed by Ryu [Phys. Rev. B 79, 075124, (2009)]. The entanglement entropy in this model separates into a contribution from a $Z_2$ gauge field and that of a system of hopping Majorana fermions, similar to what occurs in the Kitaev model. This separation enables the systematic study of the entanglement of this 3D interacting bosonic model by using the tools of non-interacting fermions. In this way, we find that the topological entanglement entropy comes exclusively from the $Z_2$ gauge field, and that it is the same for all of the phases of the system. There are differences, however, in the entanglement spectrum of the Majorana fermions that distinguish between the topologically distinct phases of the model. We further point out that the effect of introducing vortex lines in the $Z_2$ gauge field will only change the entanglement contribution of the Majorana fermions. We evaluate this contribution to the entanglement which arises due to gapless Majorana modes that are trapped by the vortex lines.Comment: 25 pages, 5 figures. Invited article to JSTAT Special Issue: Quantum Entanglement in Condensed Matter Physic

Coulomb correlations of a few body system of spatially separated charges

A Hartree-Fock and Hartree-Fock-Bogoliubov study of a few body system of spatially separated charge carriers was carried out. Using these variational states, we compute an approximation to the correlation energy of a finite system of electron-hole pairs. This energy is shown as a function of the Coulomb coupling and the interplane distance. We discuss how the correlation energy can be used to theoretically determine the formation of indirect excitons in semiconductors which is relevant for collective phenomena such as Bose-Einstein condensation (BEC).Comment: Conference EDISON16 (2009), 4 page

Delocalization phenomena in strongly disordered systems

In this dissertation, we study delocalization mechanisms in strongly disordered systems. We focus on one-dimensional systems where the localizing effects of disorder are strongest. Our explorations of delocalization mechanisms will reveal new insights into the nature of Anderson transitions in the context of the entanglement, topology and interactions. We begin by proposing momentum entanglement as an efficient tool for detecting delocalized states in a broad class of disordered systems that undergo metal-insulator transitions. We find that the signatures of delocalized states in the momentum entanglement are remarkably clear. We explain this structure in the momentum entanglement by elucidating the underlying mechanism for delocalization in these disordered models. We will afterwards discuss a different type of delocalized state that arises at disorder-induced topological phase transitions. Anderson transitions in this case occur between insulating phases, with the emergence of critical states at the transition point. Through a mapping to a disordered spin chain, we provide a real-space description of the topology of the ground state and the delocalized state that emerges at the critical point. In this case, the mechanism that leads to delocalization reveals an unconventional type of disorder-induced topological phase transition that is fundamentally different, for example, from quantum Hall transitions. Finally, we examine delocalization processes in strongly interacting many-body localized phases. We find that strong interactions and the presence of symmetry constraints lead to an important spectral asymmetry in the localization transition. This asymmetry arises from the different dynamical properties of short-ranged correlated states that form due to having strong interactions. We explain how this asymmetry presents advantages in the numerical as well as experimental study of many-body localization transitions

Many-body mobility edge due to symmetry-constrained dynamics and strong interactions

We provide numerical evidence combined with an analytical understanding of the many-body mobility edge for the strongly anisotropic spin-1/2 XXZ model in a random magnetic field. The system dynamics can be understood in terms of symmetry-constrained excitations about parent states with ferromagnetic and anti-ferromagnetic short range order. These two regimes yield vastly different dynamics producing an observable, tunable many-body mobility edge. We compute a set of diagnostic quantities that verify the presence of the mobility edge and discuss how weakly correlated disorder can tune the mobility edge further.Comment: 10 pages, 5 figure