相关论文: Rational indices for quantum ground state sectors

We introduce the index $\mathcal{N}(\omega_1,\omega_2)$ of a pair of pure states on a unital C*-algebra, which is a generalization of the notion of the index of a pair of projections on a Hilbert space. We then show that the Hall…

In this paper, I give an overview of some selected results in quantum many body theory, lying at the interface between mathematical quantum statistical mechanics and condensed matter theory. In particular, I discuss some recent results on…

We present a possible definition of a mobility gap for a many-body quantum system, in analogy to definitions of dynamical localization for single particle systems. Using this definition, we construct "corrected" quasi-adiabatic continuation…

By coupling with a qubit, we demonstrate that qubit decoherence can unambiguously detect the occurrence of ground-state degeneracy in many-body systems. We first demonstrate universality using the two-band model. Consequently, several…

We propose a quantum stripe (smectic) coupled-Luttinger-liquid model for the anisotropic states which occur in two-dimensional electron systems with high-index partial Landau level filling, $\nu^{*} = \nu - \lbrack\nu\rbrack$. Perturbative…

The quantum Hall effect is studied in a spherical geometry using the Dirac operator for non-interacting fermions in a background magnetic field, which is supplied by a Wu-Yang magnetic monopole at the centre of the sphere. Wave functions…

We use the Ward identities corresponding to general linear transformations, and derive relations between transport coefficients of $(2+1)$-dimensional systems. Our analysis includes relativistic and Galilean invariant systems, as well as…

I review why and how physical states with fractional quantum numbers can occur, emphasizing basic mechanisms in simple contexts. The general mechanism of charge fractionalization is the passage from states created by local action of fields…

The microscopic approach of Murthy and Shankar, which has recently been used to calculate the transport gaps of quantum Hall states with fractions p/(2ps+1), also implies scaling relations between gaps within a single sequence (fixed s) as…

We show via tensor network methods that the Harper-Hofstadter Hamiltonian for hard-core bosons on a square geometry supports a topological phase realizing the $\nu=1/2$ fractional quantum Hall effect on the lattice. We address the…

These lecture notes focus on the application of ideas of locality, in particular Lieb-Robinson bounds, to quantum many-body systems. We consider applications including correlation decay, topological order, a higher dimensional…

We investigate the ground state properties of a bosonic Harper-Hofstadter model with local interactions on a finite cylindrical lattice with filling fraction $\nu=1/2$. We find that our system supports topologically ordered states by…

We consider the relationship between correlations and entanglement in gapped quantum systems, with application to matrix product state representations. We prove that there exist gapped one-dimensional local Hamiltonians such that the…

We report on the properties of a system of interacting electrons in a narrow channel in the quantum Hall effect regime. It is shown that an increase in the strength of the Coulomb interaction causes abrupt changes in the width of the…

We introduce a general analytic approach to the study of factorization points and factorized ground states in quantum cooperative systems. The method allows to determine rigorously existence, location, and exact form of separable ground…

We construct an explicit duality between the interacting quantum Hall system in the lowest Landau level and a non-interacting Landau problem. This is done by absorbing the interaction into the gauge field in the form of an effective…

We construct a set of exact ground states with a localized ferromagnetic domain wall and an extended spiral structure in a quasi-one-dimensional deformed flat-band Hubbard model. In the case of quarter filling, we show the uniqueness of the…

Explicit wave functions for the hierarchy of fractionally quantized Hall states are proposed, and a method for integrating out the quasiparticle coordinates in the spherical geometry is developed. Their energies and overlaps with the exact…

We theoretically investigate quantum transport properties of quantum anomalous Hall bilayers, with arbitrary ratio of lattice constants, i.e., with lattice mismatch. In the simplest case of ratio 1 (but with different model parameters in…

We define the notion of index-module for a couple of A-lattices in a vector space, A being a Dedekind ring. We apply this notion to prove by elementary means that a weak Gras conjecture (i.e for irreducible nontrivial Q-characters) holds…