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Numerical results for the energy spectra of $N$ electrons on a spherical surface are used as input data to determine the quasiparticle energies and the pairwise ``Fermi liquid'' interactions of composite Fermion (CF) excitations in…
The physics of two-dimensional electron gas in a perpendicular magnetic field, i.e., the quantum Hall system, is remarkably rich. At half filling of the lowest Landau level, it has been predicted that ``composite fermions'' -- emergent…
We study the electron spectral function of various zero-temperature spin-charge separated phases in two dimensions. In these phases, the electron is not a fundamental excitation of the system, but rather ``decays'' into a spin-1/2…
The theoretical understanding of emergent phenomena in quantum materials is one of the greatest challenges in condensed matter physics. In contrast to simple materials such as noble metals and semiconductors, macroscopic properties of…
The quantum spin hall (QSH) phase, also known as the 2D topological insulator, is characterized by protected helical edge modes arising from time reversal symmetry. While initially proposed for band insulators, this phase can also manifest…
Electronic states with non-trivial topology host a number of novel phenomena with potential for revolutionizing information technology. The quantum anomalous Hall effect provides spin-polarized dissipation-free transport of electrons, while…
The character of the ground state of an antiferromagnetic insulator is fundamentally altered upon addition of even a small amount of charge. The added charges agglomerate along domain walls at which the spin correlations, which may or may…
Four-Fermi quantum field theories in (2+1) dimensions lie among the simplest models in high-energy physics, the understanding of which requires a non-perturbative lattice formulation addressing their strongly-coupled fixed points. These…
Topological magnetic insulators host chiral gapless edge modes. In the presence of strong interaction effects, the spin of these modes may fractionalize. Studying a 2D array of coupled insulating spin-1/2 chains, we show how spatially…
Starting from a collective description of the incompressible fractional quantum Hall liquid as an elastic medium that supports gapped neutral excitations I show that the one-electron spectral function of this system exhibits a sharp peak at…
We investigate the ground state of a balanced electron-hole system in the quantum Hall regime using mean-field theory and obtain a rich phase diagram as a function of interlayer distance d and the filling factor within a layer. We identify…
Coulomb attraction between electrons and holes in a narrow-gap semiconductor or a semimetal is predicted to lead to an elusive phase of matter dubbed 'excitonic insulator'. However, direct observation of such electronic instability remains…
Electronic stripe/nematic phases are fascinating strongly-correlated states characterized by spontaneous rotational symmetry breaking. In the quantum Hall regime, such phases typically emerge at half-filled, high-orbital-index ($N\geq2$)…
In metals, electrons in a magnetic field undergo cyclotron motion, leading to oscillations in physical properties called quantum oscillations. This phenomenon has never been seen in a robust insulator because there are no mobile electrons.…
We present a general introduction to the non-zero temperature dynamic and transport properties of low-dimensional systems near a quantum phase transition. Basic results are reviewed in the context of experiments on the spin-ladder…
The neutral fermionic edge mode is essential to the non-Abelian topological property and its experimental detection in $Z_k$ fractional quantum Hall (FQH) state for $k > 1$. Usually, the identification of the edge modes in a finite size…
In this paper, starting from a lattice model of topological insulators, we study the quantum phase transitions among different quantum states, including quantum spin Hall state, quantum anomalous Hall state and normal band insulator state…
Flat electronic bands strongly enhance Coulomb interactions and can stabilize unconventional insulating states. Motivated by the recent discovery of flat bands in breathing Kagome lattices, we use first-principles GW--Bethe--Salpeter theory…
Two-dimensional materials offer a novel platform for the development of future quantum technologies. However, the electrical characterisation of topological insulating states, non-local resistance and bandgap tuning in atomically-thin…
Strongly correlated quantum systems can exhibit exotic behavior controlled by topology. We predict that the \nu=1/2 fractional Chern insulator arises naturally in a two-dimensional array of driven, dipolar-interacting spins. As a specific…