Related papers: Large-$S$ and tensor-network methods for strongly-…
We investigate, by means of a field-theory analysis combined with the density-matrix renormalization group (DMRG) method, a theoretical model for a strongly correlated quantum system in one dimension realizing a topologically-ordered…
We study the magnetic interactions in Mott-Hubbard systems with partially filled $t_{2g}$-levels and with strong spin-orbit coupling. The latter entangles the spin and orbital spaces, and leads to a rich variety of the low energy…
The interplay between topology and correlation lies at the forefront of modern condensed matter physics. In this paper, we study the extended fermion-Hubbard model, including the on-site as well as the nearest-neighbor repulsive…
We propose a realistic scheme to quantum simulate the so-far experimentally unobserved topological Mott insulator phase -- an interaction-driven topological insulator -- using cold atoms in an optical Lieb lattice. To this end, we study a…
We have simulated a half-filled $1D$ $p$-wave periodic Anderson model with numerically exact projector quantum Monte Carlo technique, and the system is indeed located in the Haldane-like state as detected in previous works on the $p$-wave…
We extend the previous study of extracting crystalline symmetry-protected topological invariants to the correlated regime. We construct the interacting Hofstadter model defined on square lattice with the rotation and translation symmetry…
The Hubbard model is a longstanding problem in the theory of strongly correlated electrons and a very active one in the experiments with ultracold fermionic atoms. Motivated by current and prospective quantum simulations, we apply a…
We investigate the effects of electronic correlations on the Bernevig-Hughes-Zhang model using the real-space density matrix renormalization group (DMRG) algorithm. We introduce a method to probe topological phase transitions in systems…
Presented in this thesis are a set of projects which lie at the intersection between strong correlations and topological phases of matter. The first of these projects is a treatment of an infinite dimensional generalization of the SSH model…
The interacting SSH model provides an ideal ground to study the interplay between topologically insulating phases and electron-electron interactions. We study the polarization density as a topological invariant and provide an analytic…
Topological insulators have become one of the most active research areas in condensed matter physics. This article reviews progress on the topic of electronic correlations effects in the two-dimensional case, with a focus on systems with…
Physical phenomena driven by topological properties, such as the quantum Hall effect, have the appealing feature to be robust with respect to external perturbations. Lately, a new class of materials has emerged manifesting their topological…
Exploring topological phases in interacting systems is a challenging task. We investigate many-body topological physics of interacting fermions in an extended Su-Schrieffer-Heeger (SSH) model, which extends the two sublattices of SSH model…
Two-dimensional topological insulators possess conducting edge states at their boundary while being insulating in the bulk. The detection of edge states remains an open question in ultracold atom setups. We propose a configuration to…
Recent developments in analog quantum simulators based on cold atoms and trapped ions call for cross-validating the accuracy of quantum-simulation experiments with use of quantitative numerical methods; however, it is particularly…
The fermionic Hubbard model plays a fundamental role in the description of strongly correlated materials. Here we report on the realization of this Hamiltonian using a repulsively interacting spin mixture of ultracold $^{40}$K atoms in a 3D…
We analyze the high-temperature conductivity in one-dimensional integrable models of interacting fermions: the t-V model (anisotropic Heisenberg spin chain) and the Hubbard model, at half-filling in the regime corresponding to insulating…
The discovery of topological matter has revolutionized the field of condensed matter physics giving rise to many interesting phenomena, and fostering the development of new quantum technologies. In this thesis we study the quantum dynamics…
We design an interaction-driven topological insulator for fermionic cold atoms in an optical lattice, that is, we pose the question of whether we can realize in a continuous space a spontaneous symmetry breaking induced by the inter-atom…
Geometric properties of waves and wave functions can explain the appearance of integer-valued observables throughout physics. For example, these 'topological' invariants describe the plateaux observed in the quantised Hall effect and the…