Related papers: Modeling Quantum Geometry for Fractional Chern Ins…
Fractional Chern insulators (FCIs) are lattice analogs of fractional quantum Hall systems, where the interplay of strong interactions with a frustrated tunnelling kinetics leads to the emergence of a gapped ground state with long-range…
Recent developments in fractional quantum Hall (FQH) physics highlight the importance of studying FQH phases of particles partially occupying energy bands that are not Landau levels. FQH phases in the regime of strong lattice effects,…
Topologically protected edge state transport in quantum materials is dissipationless and features quantized Hall conductance, and shows great potential in highly fault-tolerant computing technologies. However, it remains elusive about how…
The Harper-Hofstadter model provides a fractal spectrum containing topological bands of any integer Chern number, $C$. We study the many-body physics that is realized by interacting particles occupying Harper-Hofstadter bands with $|C|>1$.…
We provide a detailed study of the Abelian quasiholes of $\nu=1/2$ bosonic fractional quantum Hall states on the torus geometry and in fractional Chern insulators. We find that the density distribution of a quasihole in a fractional Chern…
The realization of artificial gauge fields in ultracold atomic gases has opened up a path towards experimental studies of topological insulators and, as an ultimate goal, topological quantum matter in many-body systems. As an alternative to…
Two-dimensional moire materials present unprecedented opportunities to explore quantum phases of matter arising from the interplay of band topology and strong correlations.One of the most striking examples is the recent observation of…
We relate the collective dynamic internal geometric degrees of freedom to the gauge fluctuations in $\nu=1/m$(m odd) fractional quantum Hall effects. In this way, in the lowest Landau level, a highly nontrivial quantum geometry in…
Moir{\'e} superlattice realized in two-dimensional heterostructures offers an exciting platform to access strongly-correlated electronic states. In this work, we study transition metal dichalcogenides (TMD) Moir{\'e} superlattices with…
Two-band Chern insulators are topologically classified by the Chern number, $c$, which is given by the integral of the Berry curvature of the occupied band over the Brillouin torus. The curvature itself comes from the imaginary part of a…
We construct a class of lattice Hamiltonians whose single-particle spectrum consists of an arbitrary number of exactly degenerate flat bands that reproduce the analytic structure of the first $p$ Landau levels restricted to the lattice.…
We construct a two-band lattice model whose bands can carry the Chern numbers C=0,pm1,pm2. By means of numerical exact diagonalization, we show that the most favorable situation that selects fractional Chern insulators (FCIs) is not…
Electronic bands featuring nontrivial bulk topological invariant manifest through robust gapless modes at the boundaries, e.g., edges and surfaces. As such this bulk-boundary correspondence is also operative in driven quantum materials. For…
The discovery that the band structure of electronic insulators may be topologically non-trivial has unveiled distinct phases of electronic matter with novel properties. Recently, mechanical lattices have been found to have similarly rich…
The energy and entanglement spectrum of fractionally filled interacting topological insulators exhibit a peculiar manifold of low energy states separated by a gap from a high energy set of spurious states. In the current manuscript, we show…
Recent observations of the fractional anomalous quantum Hall effect in moir\'e materials have reignited the interest in fractional Chern insulators (FCIs). The chiral limit in which analytic Landau level-like single-particle states form an…
The isospin flavors in condensed matters can be continuously broken, forming various symmetry-broken quantum states. In moir\'e crystals, the competition between different isospin configurations can be effectively tuned by the twist angles…
Recent experiments in moir\'e quantum materials exhibit quantized Hall states without an external magnetic field, motivating continuum mechanisms based on smooth moir\'e-periodic pseudospin textures. We present a controlled theory of…
In this paper we construct fully symmetric wavefunctions for the spin-polarized fractional Chern insulators (FCI) and time-reversal-invariant fractional topological insulators (FTI) in two dimensions using the parton approach. We show that…
Correlated physics in nearly flat topological bands is a central theme in the study of moir\'e materials. While ground states at integer fillings are typically identified as quantum Hall ferromagnets within a Hartree-Fock framework, we…