Related papers: A recipe for topological observables of density ma…
Understanding the geometric information contained in quantum states is valuable in various branches of physics, particularly in solid-state physics when Bloch states play a crucial role. While the Fubini-Study metric and Berry curvature…
We present an approach of constructing invariants under local unitary transformations for multipartite quantum systems. The invariants constructed in this way can be complement to that in [Science 340 (2013) 1205-1208]. Detailed examples…
Quantum metrology is deeply connected to quantum geometry, through the fundamental notion of quantum Fisher information. Inspired by advances in topological matter, it was recently suggested that the Berry curvature and Chern numbers of…
The state of a quantum system, adiabatically driven in a cycle, may acquire a measurable phase depending only on the closed trajectory in parameter space. Such geometric phases are ubiquitous, and also underline the physics of robust…
Motivated by the recent theoretical and experimental progress in implementing topological orders with photons, we analyze photonic systems with different topologies and present a scheme to probe their topological features. Specifically, we…
Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree of freedom. This allows to define…
The standard approach to characterizing topological matter, computing topological invariants, fails when the symmetry protecting the topological phase is preserved only on average in a disordered system. Because topological invariants rely…
Ultracold atoms in optical lattices form a clean quantum simulator platform which can be utilized to examine topological phenomena and test exotic topological materials. Here we propose an experimental scheme to measure the Chern numbers of…
The discovery of topological insulators has reformed modern materials science, promising to be a platform for tabletop relativistic physics, electronic transport without scattering, and stable quantum computation. Topological invariants are…
Topologically ordered states are among the most interesting quantum phases of matter that host emergent quasi-particles having fractional charge and obeying fractional quantum statistics. Theoretical study of such states is however…
The topological order of a (2+1)D topological phase of matter is characterized by its chiral central charge and a unitary modular tensor category that describes the universal fusion and braiding properties of its anyonic quasiparticles. I…
Quantum systems of indistinguishable particles are commonly described using the formalism of second quantisation, which relies on the assumption that any admissible quantum state must be either symmetric or anti-symmetric under particle…
A concrete strategy is presented for generating strong topological insulators in $d+d'$ dimensions which have quantized physics in $d$ dimensions. Here, $d$ counts the physical and $d'$ the virtual dimensions. It consists of seeking…
Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…
Topological invariants, such as the Chern number, characterise topological phases of matter. Here we provide a method to detect Chern numbers in systems with two distinct species of fermion, such as spins, orbitals or several atomic states.…
Topology manifesting in many branches of physics deepens our understanding on state of matters. Topological photonics has recently become a rapidly growing field since artificial photonic structures can be well designed and constructed to…
We consider the problem of designing an optimal quantum detector with a fixed rate of inconclusive results that maximizes the probability of correct detection, when distinguishing between a collection of mixed quantum states. We develop a…
$U(N)^{\otimes r} \otimes O(N)^{\otimes q}$ invariants are constructed by contractions of complex tensors of order $r+q$, also denoted $(r,q)$. These tensors transform under $r$ fundamental representations of the unitary group $U(N)$ and…
The study of spatial symmetries was accomplished during the last century, and had greatly improved our understanding of the properties of solids. Nowadays, the symmetry data of any crystal can be readily extracted from standard…
We aim at reducing the uncertainties inherent in the analysis of the topological structure by using scale controlled smoothing and observables independent on the "microscopic" description of the instanton ensemble.