相关论文: Geometric Defects in Quantum Hall States

In this paper, we apply techniques of geometric quantization to study the response of the integer and fractional quantum Hall effects to toroidal geometry deformation. The main method is that of using complex time Hamiltonian evolution to…

The robustness of fractional quantum Hall states is measured as the energy gap separating the Laughlin ground-state from excitations. Using thermodynamic approximations for the correlation functions of the Laughlin state and the quasihole…

Fractional quantum Hall (FQH) fluids host quasiparticle excitations that carry a fraction of the electronic charge. Moreover, in contrast to bosons and fermions that carry exchange statistics of $0$ and $\pi$ respectively, these…

We present explicit wavefunctions for quasi-hole excitations over a variety of non-abelian quantum Hall states: the Read-Rezayi states with k\geq 3 clustering properties and a paired spin-singlet quantum Hall state. Quasi-holes over these…

For a given parent fractional quantum Hall (FQH) state at filling fraction $\nu$, the hierarchy construction produces FQH states at nearby filling fractions $\{\nu_n\}$ by condensing minimally charged quasiholes or quasiparticles of the…

We propose a geometric description of all gapped excitations in fractional quantum Hall phases that reveals several fundamental understandings with experimental consequences. These include a duality between the Hilbert space of multiple…

We discuss a quasi-particle formulation of effective edge theories for the fractional quantum Hall effect. Fundamental quasi-particles for the Laughlin state with filling fraction \nu =1/3 are edge electrons of charge -e and edge…

We show that universal transport coefficients of the fractional quantum Hall effect (FQHE) can be understood as a response to variations of spatial geometry. Some transport properties are essentially governed by the gravitational anomaly.…

We study the spin of the localised quasiparticle excitations of lowest-Landau-level quantum Hall states defined on a disk. The spin that we propose satisfies the spin-statistics relation and can be used to reconstruct the topological…

We describe the mathematical theory of topological quantum computing with symmetry defects in the language of fusion categories and unitary representations. Symmetry defects together with anyons are modeled by G-crossed braided extensions…

Fractional quantum Hall quasiparticles are generally characterized by two quantum numbers: electric charge $Q$ and scaling dimension $\Delta$. For the simplest states (such as the Laughlin series) the scaling dimension determines the…

Exchange statistics are a fundamental principle of quantum mechanics, dictating the symmetry of identical particle wavefunctions and thereby enabling emergent phenomena of many-body quantum states. The exchange-induced unitary…

We propose a family of Abelian quantum Hall states termed the non-diagonal states, which arise at filling factors $\nu=p/2q$ for bosonic systems and $\nu=p/(p+2q)$ for fermionic systems, with $p$ and $q$ being two coprime integers.…

We provide a detailed explanation of the formalism necessary to construct matrix product states for non-Abelian quasiholes in fractional quantum Hall model states. Our construction yields an efficient representation of the wave functions…

In this paper, we report on the study of Abelian and non-Abelian statistics through Fabry-Perot interferometry of fractional quantum Hall (FQH) systems. Our detection of phase slips in quantum interference experiments demonstrates a…

We study four-dimensional fractional quantum Hall states on CP2 geometry from microscopic approaches. While in 2d the standard Laughlin wave function, given by a power of Vandermonde determinant, admits a product representation in terms of…

In two dimensions, the laws of physics permit existence of anyons, particles with fractional statistics which is neither Fermi nor Bose. That is, upon exchange of two such particles, the quantum state of a system acquires a phase which is…

It has recently been pointed out that phases of matter with intrinsic topological order, like the fractional quantum Hall states, have an extra dynamical degree of freedom that corresponds to quantum geometry. Here we perform extensive…

Some models of the 5/2 fractional quantum Hall state predict that the quasi-particles, which carry the charge, have non-Abelian statistics: exchange of two quasi-particles changes the wave function more dramatically than just the usual…

We present a formal geometric framework for the study of adiabatic quantum mechanics for arbitrary finite-dimensional non-degenerate Hamiltonians. This framework generalizes earlier holonomy interpretations of the geometric phase to…