相关论文: Chern classes of Laughlin bundles on the quasihole…
The so-called multilayer wave functions were introduced in the study of the fractional Quantum Hall effect by Halperin and others. They are defined with the help of a symmetric matrix $K$ in $M^k(\mathbb{N})$, which encodes the couplings…
We begin by explaining how a physical problem of studying the quantum Hall effect on a closed surface $C$ leads, via Laughlin's approach, to a mathematical question of describing the rank and the first Chern class of a particular vector…
We perform an exact-diagonalization study of quasihole excitations for the two-component Halperin $(221)$ state in the lowest Landau level and for several $\nu=1/3$ bosonic fractional Chern insulators in topological flat bands with Chern…
We introduce a supersymmetric Chern-Simons theory whose low energy physics is that of the fractional quantum Hall effect. The supersymmetry allows us to solve the theory analytically. We quantise the vortices and, by relating their dynamics…
We study four different models of Chern insulators in the presence of strong electronic repulsion at partial fillings. We observe that all cases exhibit a Laughlin-like phase at filling fraction 1/3. We provide evidence of such a strongly…
For a discrete group $\Gamma$, we study vector bundles $E_\rho$ on compact subsets of $B\Gamma$ associated to almost representations $\rho:\Gamma \to U(n)$. We compute the first Chern class of $E_\rho$ in terms of $\rho$. When $\rho$ is…
It has been recently realized that strong interactions in topological Bloch bands give rise to the appearance of novel states of matter. Here we study connections between these systems -- fractional Chern insulators and the fractional…
Chern insulators are band insulators exhibiting a nonzero Hall conductance but preserving the lattice translational symmetry. We conclusively show that a partially filled Chern insulator at 1/3 filling exhibits a fractional quantum Hall…
We show that under some assumptions on the monodromy group some combinations of higher Chern classes of flat vector bundles are torsion in the Chow group. Similar results hold for flat vector bundles that deform to such flat vector bundles…
We study the nearly-degenerate quasihole manifold of the bosonic Hofstadter-Hubbard model on a torus, known to host the lattice analog of the Laughlin state at filling fraction $\nu = 1/2$. Away from $\nu = 1/2$ and in the presence of both…
Complex Chern-Simons bundles are line bundles with connection, originating in the study of quantization of moduli spaces of flat connections with complex gauge groups. In this paper we introduce and study these bundles in the families…
We generalize the flux insertion argument due to Laughlin, Niu-Thouless-Tao-Wu, and Avron-Seiler-Zograf to the case of fractional quantum Hall states on a higher-genus surface. We propose this setting as a test to characterise the…
We provide a formula for the Chern character of a holomorphic vector bundle in the hyper-cohomology of the de Rham complex of holomorphic sheaves on a complex manifold. This Chern character can be thought of as a completion of the Chern…
Starting from Laughlin type wave functions with generalized periodic boundary conditions describing the degenerate groundstate of a quantum Hall system we explictly construct $r$ dimensional vector bundles. It turns out that the filling…
A cocycle $\Omega: P \times G \to H$ taking values in a Lie group $H$ for a free right action of $G$ on $P$ defines a principal bundle $Q$ with the structure group $H$ over $P/G.$ The Chern character of a vector bundle associated to $Q$…
A Chern insulator (quantum anomalous Hall insulator) phase is demonstrated to exist in a typical semi-Dirac system, the TiO2/VO2 heterostructure. By combining first-principles calculations with Wannier-based tight-binding model, we…
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…
Let M be the total space of a negative line bundle over a closed symplectic manifold. We prove that the quotient of quantum cohomology by the kernel of a power of quantum cup product by the first Chern class of the line bundle is isomorphic…
A set of recent results indicates that fractionally filled bands of Chern insulators in two dimensions support fractional quantum Hall states analogous to those found in fractionally filled Landau levels. We provide an understanding of…
We devise local lattice models whose ground states are model fractional Chern insulators---Abelian and non-Abelian topologically ordered states characterized by exact ground state degeneracies at any finite size and infinite entanglement…