Related papers: Geometric bound on structure factor

In 1993 Keski-Vakkuri and Wen introduced a model for the fractional quantum Hall effect based on multilayer two-dimensional electron systems satisfying quasi-periodic boundary conditions. Such a model is essentially specified by a choice of…

We propose the notion of integrable boundary in the context of discrete integrable systems on quad-graphs. The equation characterizing the boundary must satisfy a compatibility equation with the one characterizing the bulk that we called…

Topological insulators and their intriguing edge states can be understood in a single-particle picture and can as such be exhaustively classified. Interactions significantly complicate this picture and can lead to entirely new insulating…

We prove that a spectral gap-filling phenomenon occurs whenever a Hamiltonian operator encounters a coarse index obstruction upon compression to a domain with boundary. Furthermore, the gap-filling spectra contribute to quantised current…

The presence of localized boundary modes is an unambiguous hallmark of topological quantum matter. While these modes are typically protected by topological invariants such as the Chern number, here we demonstrate that the {\it quantum…

The role of the QCD theta-parameter is investigated in pure Yang-Mills theory in the spacetime given by the four-dimensional Euclidean torus. While in this setting the introduction of possibly unphysical boundary conditions is avoided, it…

Let (M,g) be a compact Einstein manifold with smooth boundary. We consider the spectrum of the p form valued Laplacian with respect to a suitable boundary condition. We show that certain geometric properties of the boundary may be…

We characterize which cobounded quasigeodesics in the Teichmueller space T of a closed surface are at bounded distance from a geodesic. More generally, given a cobounded lipschitz path gamma in T, we show that gamma is a quasigeodesic with…

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…

We prove a nearly optimal bound on the number of stable homotopy types occurring in a k-parameter semi-algebraic family of sets in $\R^\ell$, each defined in terms of m quadratic inequalities. Our bound is exponential in k and m, but…

The motion of a quantum particle constrained to a two-dimensional non-compact Riemannian manifold with non-trivial metric can be described by a flat-space Schroedinger-type equation at the cost of introducing local mass and metric and…

We construct an algebraic description for the ground state and for the static response of the quantum Hall plateaux with filling factor $\nu=N/(2N+1)$ in the large $N$ limit. By analyzing the algebra of the fluctuations of the shape of the…

We study the quantum metric tensor and its scalar curvature for a particular version of the Lipkin-Meshkov-Glick model. We build the classical Hamiltonian using Bloch coherent states and find its stationary points. They exhibit the presence…

Berry phases and the quantum-information theoretic notion of fidelity have been recently used to analyze quantum phase transitions from a geometrical perspective. In this paper we unify these two approaches showing that the underlying…

We investigate some important physical aspects of a recently presented interior solution for the Kerr metric. It is shown that, as in the spherically symmetric case, there is a specific limit for the maximal value of the surface potential…

For a wide class of noninteracting tight-binding models in one dimension we present an analytical solution for all scattering and edge states on a half-infinite system. Without assuming any symmetry constraints we consider models with…

We show that a Laplace isospectral family of two dimensional Riemannian orbifolds, sharing a lower bound on sectional curvature, contains orbifolds of only a finite number of orbifold category diffeomorphism types. We also show that…

We show that conservation laws in quantum mechanics naturally lead to metric spaces for the set of related physical quantities. All such metric spaces have an "onion-shell" geometry. We demonstrate the power of this approach by considering…

Starting from a dynamical system $(\Omega,G)$, with $G$ a generic topological group, we devise algorithms that generate families of patterns in the Euclidean space, which densely embed $G$ and on which $G$ acts continuously by rigid shifts.…

We consider quantum Hall states on a space with boundary, focusing on the aspects of the edge physics which are completely determined by the symmetries of the problem. There are four distinct terms of Chern-Simons type that appear in the…