Related papers: Unveiling Topological Fusion in Quantum Hall Syste…
In this paper we review some connections recently discovered between topological insulators and certain classes of quantum spin liquids, focusing on two and three spatial dimensions. In two dimensions we show the integer quantum Hall effect…
We derive single-particle and two-particle correlators of anyons in the presence of a magnetic field in the lowest Landau level. We show that the two-particle correlator exhibits signatures of fractional statistics which can distinguish…
In interacting topological systems, Landau-like order parameters interplay with the band topology of fermions. The physics of domain formation in such systems can get significantly altered due to the presence of topological fermions. In…
The structural parameters of alpha helix and some forms of DNA-structures are determined by methods of algebraic topology. These structures are locally periodic and correspond to the bifurcation point for minimal surfaces given by…
The non-Abelian geometric phases of the robust degenerate ground states were proposed as physically measurable defining properties of topological order in 1990. In this paper we discuss in detail such a quantitative characterization of…
We study quantum Hall states for two-component particles (hardcore bosons and fermions) loading in topological lattice models. By tuning the interplay of interspecies and intraspecies interactions, we demonstrate that two-component…
The abelian hierarchy of quantum Hall states accounts for most of the states in the lowest Landau level, and there is evidence of a similar hierarchy of non-abelian states emanating from the {\nu} = 5/2 Moore-Read state in the second Landau…
The band theory of solids is arguably the most successful theory of condensed matter physics, providing the description of the electronic energy levels in a variety of materials. Electronic wavefunctions obtained from the band theory allow…
A key property of topologically ordered systems, such as Quantum Hall states, is the existence of excitations obeying fractional quantum statistics - anyons. We develop a theory for multicomponent counterflow states where an ordinary…
Modern material science has been revolutionized by the discovery of novel topological states of quantum matter, which sheds new lights on solving long-standing scientific challenges. However, the exotic quantum phenomena are typically…
For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…
We show that model states of fractional quantum Hall fluids at all experimentally detected plateau can be uniquely determined by imposing translational invariance with a particular scheme of Hilbert space truncation motivated from physical…
The role of topology in elementary quantum physics is discussed in detail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge…
Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space,…
Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no…
Topological phases supported by quasi-periodic spin-chain models and their bulk-boundary principles are investigated by numerical and K-theoretic methods. We show that, for both the un-correlated and correlated phases, the operator algebras…
The $\nu = 1$ quantum Hall ground state in materials like GaAs is well known to be ferromagnetic in nature. The exchange part of the Coulomb interaction provides the necessary attractive force to align the electron spins spontaneously. The…
Topological phases like topological insulators or superconductors are fascinating quantum states of matter, featuring novel properties such as emergent chiral edge states or Majorana fermions with non-Abelian braiding statistics. The recent…
We present a novel M-theoretic approach of constructing and classifying anyonic topological phases of matter, by establishing a correspondence between (2+1)d topological field theories and non-hyperbolic 3-manifolds. In this construction,…
A method for compiling quantum algorithms into specific braiding patterns for non-Abelian quasiparticles described by the so-called Fibonacci anyon model is developed. The method is based on the observation that a universal set of quantum…