Related papers: Local marker for interacting topological insulator…

While topology is a property of a quantum state itself, most existing methods for characterizing the topology of interacting phases of matter require direct knowledge of the underlying Hamiltonian. We offer an alternative by utilizing the…

Local topological markers are used to characterize Chern insulators in the presence of spatial inhomogeneities, such as boundaries and disorder. In this paper, we study the local Chern marker in systems with partial translational symmetry.…

Robust zero modes supported by defects is one of the key features of topological matter. Its presence renders a system topologically inhomegeneuous, thus having no well-defined global topological invariant. The quantities labeling different…

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…

Understanding how topology survives in strongly correlated systems remains a central challenge, as most topological diagnostics rely on non-interacting band structures. Here we present a framework to characterize interacting topological…

We propose a topological order parameter for interacting topological insulators, expressed in terms of the full Green's functions of the interacting system. We show that it is exactly quantized for a time reversal invariant topological…

A system having macroscopic patches in different topological phases have no well-defined global topological invariant. To treat such a case, the quantities labeling different areas of the sample according to their topological state are…

Topological states of matter exhibit many novel properties due to the presence of robust topological invariants such as the Chern index. These global characteristics pertain to the system as a whole and are not locally defined. However,…

We study effect of interactions on time-reversal-invariant topological insulators. Their topological indices are expressed by interacting Green's functions. Under the local self-energy approximation, we connect topological index and surface…

The engineering of topological non-trivial states of matter, using cold atoms, has made great progress in the last decade. Driven by experimental successes, it has become of major interest in the cold atom community. In this work we…

Synthetic dimensions provide a powerful route to engineer topological lattice models in ultracold atomic systems, but they contain intrinsic nonlocal interactions along the synthetic direction. We investigate an extended Harper-Hofstadter…

Two-dimensional topological insulators possess conducting edge states at their boundary while being insulating in the bulk. The detection of edge states remains an open question in ultracold atom setups. We propose a configuration to…

The organization of the electrons in the ground state is classified by means of topological invariants, defined as global properties of the wavefunction. Here we address the Chern number of a two-dimensional insulator and we show that the…

A central property of Chern insulators is the robustness of the topological phase and edge states to impurities in the system. Despite this, Chern number cannot be straightforwardly calculated in the presence of disorder. Recently, work has…

This contribution describes the mathematical theory of topological indices in solid state systems composed of non-interacting Fermions. In particular, this covers the spectral localizer and the bulk-boundary correspondence.

We construct a Green function, which can identify the topological nature of interacting systems. It is equivalent to the single-particle Green function of effective non-interacting particles, the Bloch Hamiltonian of which is given by the…

An insulator differs from a metal because of a different organization of the electrons in their ground state. In recent years this feature has been probed by means of a geometrical property: the quantum metric tensor, which addresses the…

Topological insulators are noninteracting, gapped fermionic systems which have gapless boundary excitations. They are characterized by topological invariants, which can be written in many different ways, including in terms of Green's…

Local topological markers have proven to be a valuable tool for investigating systems with topologically non-trivial bands. Due to their local nature, such markers can treat translationally invariant systems and spatially inhomogeneous…

We propose general topological order parameters for interacting insulators in terms of the Green's function at zero frequency. They provide an unified description of various interacting topological insulators including the quantum anomalous…