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Understanding the effects of electron-electron interactions in half metallic magnets (HMs), which have band structures with one gapped spin channel and one metallic channel, poses fundamental theoretical issues as well as having importance…
Despite being relevant to better understand the properties of honeycomb-like systems, as graphene-based compounds, the electron-phonon interaction is commonly disregarded in theoretical approaches. That is, the effects of phonon fields on…
We study the behaviour of electrons interacting with a classical magnetic background via a strong Hund coupling. The magnetic background results from a Hamiltonian which favours at low temperature the emergence of a phase with non-zero…
Interactions are responsible for intriguing physics, e.g. emergence of exotic ground states and excitations, in a wide range of systems. Here we theoretically demonstrate that dipole-dipole interaction leads to bosonic eigen-excitations…
Twisted bilayer graphene near the magic angle is known to have a cascade of insulating phases at integer filling factors of the low-energy bands. In this Letter we address the nature of these phases through an unrestricted, large-scale…
Long-range interactions can qualitatively reorganize correlated-electron ground states. In the square-lattice Hubbard model, on-site repulsion produces antiferromagnetic spin and charge stripes upon doping. We show that including a…
By using a modulated magnetic field in a Feshbach resonance for ultracold fermionic atoms in optical lattices, we show that it is possible to engineer a class of models usually referred to as correlated-hopping models. These models differ…
A two-dimensional electron system exposed to a strong magnetic field produces a plethora of strongly interacting fractional quantum Hall (FQH) states, the complex topological orders of which are revealed through exotic emergent particles,…
Using Cluster Perturbation Theory we calculate Green's functions, quasi-particle energies and topological invariants for interacting electrons on a 2-D honeycomb lattice, with intrinsic spin-orbit coupling and on-site e-e interaction. This…
Strongly correlated electron systems host a variety of poorly understood correlations in their high temperature normal state. Unlike ordered phases defined by order parameters, these normal state phases are often defined through…
In this work, we propose an exactly solvable two-dimensional lattice model of strongly correlated electrons that realizes a quantum anomalous Hall insulator with Chern number $\mathcal{C}=1$. First, we show that the interplay of ionic…
The fractional quantum Hall effect has recently been shown to exist in heterostructures of van der Waals materials without an externally applied magnetic field, e.g. in twisted bilayers of MoTe$_2$. These fractional Chern insulators break…
A possible realization of Hall conductivity, quantized at odd integer factors of $e^2/h$ for graphene's honeycomb lattice is proposed. I argue that, in the presence of \emph{uniform} real and pseudo-magnetic fields, the valley degeneracy…
As a topological insulator, the quantum Hall (QH) effect is indexed by the Chern and spin-Chern numbers $\mathcal{C}$ and $\mathcal{C}_{\text{spin}}$. We have only $\mathcal{C}_{\text{spin}}=0$ or $\pm \frac{1}{2}$ in conventional QH…
We show that all the bands of the Hofstadter model on the torus have an exactly flat dispersion and Berry curvature when a special system size is chosen. This result holds for any hopping and Chern number. Our analysis therefore provides a…
The continuous imaginary-time quantum Monte Carlo method with the worm update algorithm is applied to explore the ground state properties of the spin-1/2 Heisenberg model with antiferromagnetic (AF) coupling $J>0$ and ferromagnetic (F)…
We use the quasistatic approach to analyze the criterion of ferromagnetism for two-dimensional (2D) systems with the Fermi level near Van Hove singularities (VHS) of the electronic spectrum. It is shown that the spectrum of spin excitations…
Motivated by the discovery of the quantum anomalous Hall effect in Cr-doped \ce{(Bi,Sb)2Te3} thin films, we study the generic states for magnetic topological insulators and explore the physical properties for both magnetism and itinerant…
Applying a unified approach, we study integer quantum Hall effect (IQHE) and fractional quantum Hall effect (FQHE) in the Hofstadter model with short range interaction between fermions. An effective field, that takes into account the…
The rapid development of moir\'e quantum matter has recently led to the remarkable discovery of the fractional quantum anomalous Hall effect, and sparked predictions of other novel correlation-driven topological states. Here, we investigate…