We study one-dimensional, interacting, gapped fermionic systems described by variants of the Peierls-Hubbard model and characterize their phases via a topological invariant constructed out of their Greens functions. We demonstrate that the existence
of topologically protected, zero-energy states at the boundaries of these systems can be tied to the values of their topological invariant, just like when working with the conventional, noninteracting topological insulators. We use a combination of analytical methods and the numerical density matrix renormalization group method to calculate the values of the topological invariant throughout the phase diagrams of these systems, thus deducing when topologically protected boundary states are present. We are also able to study topological states in spin systems because, deep in the Mott insulating regime, these fermionic systems reduce to spin chains. In this way, we associate the zero-energy states at the end of an antiferromagnetic spin-one Heisenberg chain with the topological invariant 2.
Using the adaptive time-dependent density matrix renormalization group, we study the time evolution of density correlations of interacting spinless fermions on a one-dimensional lattice after a sudden change in the interaction strength. Over a broad
range of model parameters, the correlation function exhibits a characteristic light-cone-like time evolution representative of a ballistic transport of information. Such behavior is observed both when quenching an insulator into the metallic region and also when quenching within the insulating region. However, when a metallic state beyond the quantum critical point is quenched deep into the insulating regime, no indication for ballistic transport is observed. Instead, stable domain walls in the density correlations emerge during the time evolution, consistent with the predictions of the Kibble-Zurek mechanism.
We investigate the effect of Dzyaloshinskii-Moriya (DM) interactions on torque measurements of quantum magnets with magnetization plateaux in the context of a frustrated spin-1/2 ladder. Using extensive DMRG simulations, we show that the DM contribut
ion to the torque is peaked at the critical fields, and that the total torque is non-monotonous if the DM interaction is large enough compared to the g-tensor anisotropy. More remarkably, if the DM vectors point in a principal direction of the g-tensor, torque measurements close to this direction will show well defined peaks even for small DM interaction, leading to a very sensitive way to detect the critical fields. We propose to test this effect in the two-dimensional plateau system SrCu$_2$(BO$_3$)$_2$.
