Related papers: Topological Matter and Fractional Entangled Quantu…
We study anisotropic lattice strips in the presence of a magnetic field in the quantum Hall effect regime. At specific magnetic fields, causing resonant Umklapp scattering, the system is gapped in the bulk and supports chiral edge states in…
Non-relativistic charged particles and strings coupled with abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. We consider three models: the string in self-interaction through a…
We develop a stochastic description of the topological properties in an interacting Chern insulator. We confirm the Mott transition's first-order nature in the interacting Haldane model on the honeycomb geometry, from a mean-field…
Topological photonics has received extensive attention from researchers because it provides brand new physical principles to manipulate light. Band topology of optical materials is characterized using the Berry phase defined by Bloch…
Topologically-ordered matter is a novel quantum state of matter observed only in a small number of physical systems, notably two-dimensional electron systems exhibiting fractional quantum Hall effects. It was recently proposed that a simple…
A model aimed at understanding quantum gravity in terms of Birkhoff's approach is discussed. The geometry of this model is constructed by using a winding map of Minkowski space into a $\mathbb{R}^{3} \times S^{1}$-cylinder. The basic field…
Topological aspects of graphene are reviewed focusing on the massless Dirac fermions with/without magnetic field. Doubled Dirac cones of graphene are topologically protected by the chiral symmetry. The quantum Hall effect of the graphene is…
The holographic duality allows to construct and study models of strongly coupled quantum matter via dual gravitational theories. In general such models are characterized by the absence of quasiparticles, hydrodynamic behavior and Planckian…
Atom optics demonstrates optical phenomena with coherent matter waves, providing a foundational connection between light and matter. Significant advances in optics have followed the realisation of structured light fields hosting complex…
Quantum metric, a fundamental component of quantum geometry, has attracted broad interest in recent years due to its critical role in various quantum phenomena. Meanwhile, band topology, which serves as an important framework in condensed…
This thesis explores the application of differential geometric and general relativistic techniques to deepen our understanding of quantum mechanical systems. We focus on three systems, employing these mathematical frameworks to uncover…
Multicomponent quantum Hall effect, under the interplay between intercomponent and intracomponent correlations, leads us to new emergent topological orders. Here, we report the theoretical discovery of fractional quantum hall effect of…
We introduce a framework for internal topological symmetries in quantum field theory, including "noninvertible symmetries" and "categorical symmetries". This leads to a calculus of topological defects which takes full advantage of…
We study the quantum mechanics of a system of topologically interacting particles in 2+1 dimensions, which is described by coupling the particles to a Chern-Simons gauge field of an inhomogeneous group. Analysis of the phase space shows…
Topological phases of matter is an exotic phenomena in modern condense matter physics, which has attracted much attention due to the unique boundary states and transport properties. Recently, this topological concept in electronic materials…
Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization…
The search for topological phases of matter is evolving towards strongly interacting systems, including magnets and superconductors, where exotic effects emerge from the quantum-level interplay between geometry, correlation and topology.…
Topological phases of matters are of fundamental interest and have promising applications. Fascinating topological properties of light have been unveiled in classical optical materials. However, the manifestation of topological physics in…
Using the idea of the degree of a smooth mapping between two manifolds of the same dimension we present here the topological (homotopical) classification of the mappings between spheres of the same dimension, vector fields, monopole and…
Topological defects in Bloch bands, such as Dirac points in graphene, and their resulting Berry phases play an important role for the electronic dynamics in solid state crystals. Such defects can arise in systems with a two-atomic basis due…