Related papers: Topological Aspects of Matters and Langlands Progr…
In the gauge theory approach to the geometric Langlands program, ramification can be described in terms of ``surface operators,'' which are supported on two-dimensional surfaces somewhat as Wilson or 't Hooft operators are supported on…
An algebraic formalism for description of quantum states of charged particle with spin moving in two-dimensional space under influence of singular magnetic field is developed in terms of graded algebras. The fundamental assumption is that…
Some algebraic issues of the FQHE are presented. First, it is shown that on the space of Laughlin wavefunctions describing the $\nu =1/m$ FQHE, there is an underlying $W_{\infty}$ algebra, which plays the role of a spectrum generating…
The fractional quantum Hall effect remains a captivating area in condensed matter physics, characterized by strongly correlated topological order, which manifests as fractionalized excitations and anyonic statistics. Numerical simulations,…
The purpose of these lectures is to describe the basic theoretical structures underlying the rich and beautiful physics of the quantum Hall effect. The focus is on the interplay between microscopic wavefunctions, long-distance effective…
We study the two-dimensional twisted (0,2) sigma-model on various smooth complex flag manifolds G/B, and explore its relevance to the geometric Langlands program. We find that an equivalence - at the level of the holomorphic chiral algebra…
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…
This article presents the basis of a theory of entanglement. We begin with a classical theory of entangled discrete measures in Section~1. Section~2 treats quantum mechanics and discusses the statistics of bounded operators on a Hilbert…
We consider spin-polarized electrons in a single Landau level on a torus. The quantum Hall problem is mapped onto a one-dimensional lattice model with lattice constant $2\pi/L_1$, where $L_1$ is a circumference of the torus (in units of the…
We study the quantum entanglement structure of integer quantum Hall states via the reduced density matrix of spatial subregions. In particular, we examine the eigenstates, spectrum and entanglement entropy (EE) of the density matrix for…
We examine various properties of double field theory and the doubled string sigma model in the context of geometric quantisation. In particular we look at T-duality as the symplectic transformation related to an alternative choice of…
In this paper, we address a foundational challenge in quantum field theory on curved spacetime by developing a consistent framework within loop quantum gravity. We introduce a methodology for defining meaningful superpositions of quantum…
Landau levels have represented a very rich field of research, which has gained widespread attention after their application to quantum Hall effect. In a particular gauge, the holomorphic gauge, they give a physical implementation of…
The Quantum Hall Effects offer a rich variety of theoretical and experimental advances. They provide interesting insights on such topics as complementarity, gauge invariance, strong interactions, emergence of new theoretical concepts. This…
Band topology and related spin (or pseudo-spin) physics of photons provide us with a new dimension for manipulating light, which is potentially useful for information communication and data storage. Especially, the quantum spin Hall effect…
This thesis discusses various aspects of duality in quantum field theory and string theory. In the first part we consider duality in topological quantum field theories, concentrating on the Donaldson and Seiberg-Witten theories as (dual)…
The phenomenon of quantum entanglement is thoroughly investigated, focussing especially on geometrical aspects and on bipartite systems. After introducing the formalism and discussing general aspects, some of the most important separability…
The phenomenological aspects of string theory are briefly reviewed. Emphasis is given to the status of 4D string model building, effective Lagrangians, model independent results, supersymmetry breaking and duality symmetries.
Recently developed strong-coupling theory open up the possibility of treating quantum-mechanical systems with hard-wall potentials via perturbation theory. To test the power of this theory we study here the exactly solvable quantum…
Quantum aspects of black holes represent an important testing ground for a theory of quantum gravity. The recent success of string theory in reproducing the Bekenstein-Hawking black hole entropy formula provides a link between general…