Related papers: Topology and geometry under the nonlinear electrom…
The optical properties of solids are governed not only by their energy band dispersions but also by the quantum geometry of Bloch states. While the role of energy bands in determining the perceived optical appearance of materials, such as…
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…
Quantum materials are driving a technology revolution in sensing, communication, and computing, while simultaneously testing many core theories of the past century. Materials such as topological insulators, complex oxides, quantum dots,…
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…
Much of our understanding of gapless quantum matter stems from low-energy descriptions using conformal field theory. This is especially true in 1+1 dimensions, where such theories have an infinite-dimensional parameter space induced by…
The control of wave scattering in complex non-Hermitian settings is an exciting subject -- often challenging the creativity of researchers and stimulating the imagination of the public. Successful outcomes include invisibility cloaks,…
Nonlinear topology is an emerging field that combines the intrinsic reconfigurability of nonlinear systems with the robustness of topological protection, offering fertile ground for unconventional phenomena and novel applications. Recently,…
One-dimensional discrete-time quantum walks show a rich spectrum of topological phases that have so far been exclusively analysed in momentum space. In this work we introduce an alternative approach to topology which is based on the…
A number of tools have been developed to detect topological phase transitions in strongly correlated quantum systems. They apply under different conditions, but do not cover the full range of many-body models. It is hence desirable to…
Exotic electronic states are realized in novel quantum materials. This field is revolutionized by the topological classification of materials. Such compounds necessarily host unique states on their boundaries. Scanning tunneling microscopy…
Topology, a well-established concept in mathematics, has nowadays become essential to describe condensed matter. At its core are chiral electron states on the bulk, surfaces and edges of the condensed matter systems, in which spin and…
An alternative model to describe the electronic and thermal properties of quantum dot based on triangle geometry is proposed. The model predicts characteristics and limitations of the system by controlling the magnetic field and…
The application of topology in optics has led to a new paradigm in developing photonic devices with robust properties against disorder. Although significant progress on topological phenomena has been achieved in the classical domain, the…
Topology is a powerful tool for categorizing magnetization textures by defining a topological index in both two-dimensional (2D) systems, such as thin films or curved surfaces, and in 3D bulk systems. In the emerging field of 3D…
Nonlinear optical frequency conversion, observed more than half a century ago, is a corner stone in modern applications of nonlinear and quantum optics. It is well known that frequency conversion processes are constrained by conservation…
We describe recent progress in our understanding of the interplay between interactions, symmetry, and topology in states of quantum matter. We focus on a minimal generalization of the celebrated topological band insulators to interacting…
We introduce the theoretical framework we use to study the bewildering variety of phases in condensed--matter physics. We emphasize the importance of the breaking of symmetries, and develop the idea of an order parameter through several…
Topology and interactions are foundational concepts in the modern understanding of quantum matter. Their nexus yields three significant research directions: competition between distinct interactions, as in the multiple intertwined phases,…
Recently, we witnessed a tremendous effort to conquer the realm of acoustics as a possible playground to test with sound waves topologically protected wave propagation. Acoustics differ substantially from photonic and electronic systems…
Combination of a construction of unambiguous quantum conditions out of the conventional one and a simultaneous quantization of the positions, momenta, angular momenta and Hamiltonian leads to the geometric potential given by the so-called…