Related papers: Floquet quantum geometry in periodically driven to…
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…
Floquet topological insulators are topological phases of matter generated by the application of time-periodic perturbations on otherwise conventional insulators. We demonstrate that spatial variations in the time-periodic potential lead to…
We propose a systematic way of constructing Floquet second-order topological insulators (SOTIs) based on time-glide symmetry, a nonsymmorphic space-time symmetry that is unique in Floquet systems. In particular, we are able to show that the…
Quantum geometry, characterized by the quantum geometric tensor, is pivotal in diverse physical phenomena in quantum materials. In condensed matter systems, quantum geometry refers to the geoemtric properties of Bloch states in the…
The manipulation of the helical edge states of two-dimensional topological insulators is crucial for the development of technological applications. Recently, an important step forward, namely, the experimental realization of a quantum point…
The formalism of continuous-time quantum walks on graphs has been widely used in the study of quantum transport of energy and information, as well as in the development of quantum algorithms. In experimental settings, however, there is…
We review methods for using time-periodic fields (e.g., laser or microwave fields) to induce non-equilibrium topological phenomena in quantum many-body systems. We discuss how such fields can be used to change the topological properties of…
Periodically driven (Floquet) systems have been under active theoretical and experimental investigations. This paper aims at a systematic study in the following aspects of Floquet systems: (i) A systematic formulation of topological…
Standard topological invariants, such as the Chern number and Berry phase, form the bedrock of modern quantum matter classification. However, we demonstrate that this framework undergoes a \textbf{catastrophic failure} in the presence of…
Anomalous Floquet topological phases are a hallmark, without a static analog, of periodically driven systems. Recently, Quantum Floquet Engineering has emerged as an interesting approach to cavity-QED materials, which recovers the physics…
Time-dependent $\mathcal{PT}$-symmetric quantum mechanics is featured by a varying inner-product metric and has stimulated a number of interesting studies beyond conventional quantum mechanics. In this paper, we explore geometric aspects of…
Topological phase transitions between a conventional insulator and a state of matter with topological properties have been proposed and observed in mercury telluride - cadmium telluride quantum wells. We show that a topological state can be…
Higher-order topological phases are characterized by protected states localized at the corners or hinges of the system. By applying time-periodic quenches to a two-dimensional lattice with balanced gain and loss, we obtain a rich variety of…
Periodic driving of a quantum system can enable new topological phases with no analog in static systems. In this paper we systematically classify one-dimensional topological and symmetry-protected topological (SPT) phases in interacting…
For time-periodical quantum systems generalized Floquet operator is found to be integral of motion.Spectrum of this invariant is shown to be quasienergy spectrum.Analogs of invariant Floquet operators are found for nonperiodical systems…
Spatially uniform excitations can induce Floquet topological bandstructures within insulators which have equal characteristics to those of topological insulators. Going beyond we demonstrate in this article the evolution of Floquet…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
Dynamical quantum phase transitions (DQPTs) are characterized by nonanalytic behaviors of physical observables as functions of time. When a system is subject to time-periodic modulations, the nonanalytic signatures of its observables could…
When a physical system is subjected to a strong external multi-frequency drive, its dynamics can be conveniently represented in the multi-dimensional Floquet lattice. The number of the Floquet lattice dimensions equals the number of {\em…
Topological phases in quantum and classical systems have been of significant recent interest due to their fascinating physical properties. While a range of different mechanisms to induce topological order have been introduced, a quest for…