Related papers: Models of Topology Change
Entanglement entropy in topologically ordered matter phases has been computed extensively using various methods. In this paper, we study the entanglement entropy of topological phases in two-spaces from a new perspective---the perspective…
Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a…
Topological quantum many-body systems, such as Hall insulators, are characterized by a hidden order encoded in the entanglement between their constituents. Entanglement entropy, an experimentally accessible single number that globally…
Tessellations of the hyperbolic spaces by regular polygons are becoming popular because they support discrete quantum and classical models displaying unique spectral and topological characteristics. Resolving the true bulk spectra and the…
We compute a momentum space version of the entanglement spectrum and entanglement entropy of general Young tableau states, and one-point functions on Young tableau states. These physical quantities are used to measure the topology of the…
We start to develop the quantization formalism in a hyperbolic Hilbert space. Generalizing Born's probability interpretation, we found that unitary transformations in such a Hilbert space represent a new class of transformations of…
We report the creation of a wide range of quantum states with controllable degrees of entanglement and entropy using an optical two-qubit source based on spontaneous parametric downconversion. The states are characterised using measures of…
We study the topological properties of one dimensional systems undergoing unitary time evolution. We show that symmetries possessed both by the initial wavefunction and by the Hamiltonian at all times may not be present in the…
In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled quantum systems to the simulation of quantum…
We study the dynamical process of equilibration of topological properties in quantum many-body systems undergoing a parameter quench between two topologically inequivalent Hamiltonians. This scenario is motivated by recent experiments on…
A general upper bound for topological entropy of switched nonlinear systems is constructed, using an asymptotic average of upper limits of the matrix measures of Jacobian matrices of strongly persistent individual modes, weighted by their…
A given fractional quantum Hall state may admit multiple, distinct edge phases on its boundary. We explore the implications that multiple edge phases have for the entanglement spectrum and entropy of a given bulk state. We describe the…
We study Hamiltonians with point interactions in spaces of vector-valued functions. Using some information from the theory of quantum graphs we describe a class of the operators which can be reduced to the direct sum of several…
The holographic prescription for computing entanglement entropy requires that the bulk extremal surface, whose area encodes the amount of entanglement, satisfies a homology constraint. Usually this is stated as the requirement of a…
We study the entanglement entropy between (possibly distinct) topological phases across an interface using an Abelian Chern-Simons description with topological boundary conditions (TBCs) at the interface. From a microscopic point of view,…
After a brief introduction to the concept of entanglement in quantum systems, I apply these ideas to many-body systems and show that the von Neumann entropy is an effective way of characterising the entanglement between the degrees of…
Bound states of two interacting particles moving on a lattice can exhibit remarkable features that are not captured by the underlying single-particle picture. Inspired by this phenomenon, we introduce a novel framework by which genuine…
We numerically investigate and experimentally demonstrate an in-situ topological band transition in a highly tunable mechanical system made of cylindrical granular particles. This system allows us to tune its inter-particle stiffness in a…
The classification of electron systems according to their topology has been at the forefront of condensed matter research in recent years. It has been found that systems of the same symmetry, previously thought of as equivalent, may in fact…
The topological R\'enyi and entanglement entropies depend on the bipartition of the manifold and the choice of the ground states. However, these entanglement quantities remain invariant under a coordinate transformation when the bipartition…