Related papers: Topological defects, fractals and the structure of…
A finite universe naturally supports chaotic classical motion. An ordered fractal emerges from the chaotic dynamics which we characterize in full for a compact 2-dimensional octagon. In the classical to quantum transition, the underlying…
Quantum correlations in compound systems are of great importance, and they are fundamental resource for the development of quantum computation protocols and quantum information. In this work we construct bipartite pure coherent states using…
Given two two-dimensional conformal field theories, a domain wall -- or defect line -- between them is called invertible if there is another defect with which it fuses to the identity defect. A defect is called topological if it is…
Quantum field theory (QFT) on fractal spacetimes is a program aiming at quantizing the gravitational interaction consistently at all energy scales thanks to an intrinsically or dynamically induced multiscale or multifractal-like spacetime…
Performing topological manipulations is a fruitful way to understand global aspects of Quantum Field Theory (QFT). Such modifications are typically controlled by the notion of Topological QFT (TQFT) coupling across different codimensions.…
Topological quantum matter exhibits a range of exotic phenomena when enriched by subdimensional symmetries. This includes new features beyond those that appear in the conventional setting of global symmetry enrichment. A recently discovered…
Nonlinear dynamics in the fundamental interaction between a two-level atom with recoil and a quantized radiation field in a high-quality cavity is studied. We consider the strongly coupled atom-field system as a quantum-classical hybrid…
Disordered hyperuniform systems are exotic states of matter that completely suppress large-scale density fluctuations like crystals, and yet possess no Bragg peaks similar to liquids or glasses. Such systems have been discovered in a…
By resorting to some results in quantum field theories with spontaneous breakdown of symmetry we show that an explanation based on microscopic dynamics can be given of the fact that topological defect formation is observed during the…
Gapped non-liquid state (also known as fracton state) is a very special gapped quantum state of matter that is characterized by a microscopic cellular structure. Such microscopic cellular structure has a macroscopic effect at arbitrary long…
"Quantum Topology" deals with the general quantum theory as the theory of the functional quantum space; space time and energy momentum forms form a connected manifold; a functional quantum space on the quantum level. The general quantum…
Coherent states, and the Hilbert space representations they generate, provide ideal tools to discuss classical/quantum relationships. In this paper we analyze three separate classical/quantum problems using coherent states, and show that…
In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction…
(2+1) dimensional topological quantum field theories with defect excitations are by now quite well understood, while many questions are still open for (3+1) dimensional TQFTs. Here we propose a strategy to lift states and operators of a…
In the first part of the paper we define a perturbative (pre-formal) geometry and formulate a theorem on the relation between the construction of a perturbative neighborhood of affine varieties and the higher tangent bundles. In the second…
We examine the interplay of symmetry and topological order in $2+1$ dimensional topological phases of matter. We present a definition of the \it topological symmetry \rm group, which characterizes the symmetry of the emergent topological…
In general quantum field theories (QFTs), ordinary (0-form) global symmetries and 1-form symmetries can combine into 2-group global symmetries. We describe this phenomenon in detail using the language of symmetry defects. We exhibit a…
Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic…
We propose a set of constraints on the ground-state wavefunctions of fracton phases, which provide a possible generalization of the string-net equations used to characterize topological orders in two spatial dimensions. Our constraint…
Various relations between conformal quantum field theories in one, two and four dimensions are explored. The intention is to obtain a better understanding of 4D CFT with the help of methods from lower dimensional CFT.