Related papers: Probing Topological Stability with Nonlocal Quantu…

Topological insulators and topological superconductors display various topological phases that are characterized by different Chern numbers or by gapless edge states. In this work we show that various quantum information methods such as the…

Coupled layer constructions are a valuable tool for capturing the universal properties of certain interacting quantum phases of matter in terms of the simpler data that characterizes the underlying layers. In the study of fracton phases,…

We propose a new viewpoint on the study of localization transitions in disordered quantum systems, showing how critical properties can be seen also as a geometric transition in the data space generated by the classically encoded…

We introduce "quantum barcodes," a theoretical framework that applies persistent homology to classify topological phases in quantum many-body systems. By mapping quantum states to classical data points through strategic observable…

Dynamical characterization of topological phases under quantum quench dynamics has been demonstrated as a powerful and efficient tool. Previous studies have been focused on systems of which the Hamiltonian consists of matrices that commute…

Topological invariants are global properties of the ground-state wave function, typically defined as winding numbers in reciprocal space. Over the years, a number of topological markers in real space have been introduced, allowing to map…

The topology of a single-particle band structure plays a fundamental role in understanding a multitude of physical phenomena. Motivated by the connection between quantum walks and such topological band structures, we demonstrate that a…

Topological properties of solid states have sparked considerable recent interest due to their importance in the physics of lattices with a non-trivial basis and their potential in the design of novel materials. Here we describe an…

The fundamental concept underlying topological phenomena posits the geometric phase associated with eigenstates. In contrast to this prevailing notion, theoretical studies on time-varying Hamiltonians allow for a new type of topological…

Topological data analysis provides a set of tools to uncover low-dimensional structure in noisy point clouds. Prominent amongst the tools is persistence homology, which summarizes birth-death times of homological features using data objects…

It is an ongoing quest to realize topologically ordered quantum states on different platforms including condensed matter systems, quantum simulators and digital quantum processors. Unlike conventional states characterized by their local…

For decades, mathematical physicists have searched for a coordinate independent quantization procedure to replace the ad hoc process of canonical quantization. This effort has largely coalesced into two distinct research programs: geometric…

Mechanical topological insulators are well understood for linear and weakly nonlinear systems, however traditional analysis methods break down for strongly nonlinear systems since linear methods can not be applied in that case. We study one…

Topological metals are special conducting materials with gapless band structures and nontrivial edge-localized resonances, whose discovery has proved elusive because the traditional topological classification methods do not apply in this…

In closed quantum systems, a dynamical phase transition is identified by nonanalytic behaviors of the return probability as a function of time. In this work, we study the nonunitary dynamics following quenches across exceptional points in a…

Topological orders can be used as media for topological quantum computing --- a promising quantum computation model due to its invulnerability against local errors. Conversely, a quantum simulator, often regarded as a quantum computing…

In topology, a torus remains invariant under certain non-trivial transformations known as modular transformations. In the context of topologically ordered quantum states of matter, these transformations encode the braiding statistics and…

Predictive geometric models deliver excellent results for many Machine Learning use cases. Despite their undoubted performance, neural predictive algorithms can show unexpected degrees of instability and variance, particularly when applied…

Quantum walks constitute a versatile platform for simulating transport phenomena on discrete graphs including topological material properties while providing a high control over the relevant parameters at the same time. To experimentally…

Quantum computers promise to perform computations beyond the reach of modern computers with profound implications for scientific research. Due to remarkable technological advances, small scale devices are now becoming available for use. One…