Related papers: Modular transformations and topological orders in …
In the last two decades, a vast variety of topological phases have been described, predicted, classified, proposed, and measured. While there is a certain unity in method and philosophy, the phenomenology differs wildly. This work deals…
We give a pedagogical introduction to topologically ordered states of matter, with the aim of familiarizing the reader with their axiomatic topological quantum field theory description. We introduce basic noninteracting topological phases…
Meaningful topological invariants for mixed quantum states are challenging to identify as there is no unique way to define them, and most choices do not directly relate to physical observables. Here, we propose a simple pragmatic approach…
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…
Electron energy bands of crystalline solids generically exhibit degeneracies called band-structure nodes. Here, we introduce non-Abelian topological charges that characterize line nodes inside the momentum space of crystalline metals with…
We develop a mathematical theory of symmetry protected trivial (SPT) orders and anomaly-free symmetry enriched topological (SET) orders in all dimensions via two different approaches with an emphasis on the second approach. The first…
The interplay between topology and nonlinearity represents a central challenge in modern physics. Here, we investigate this interplay by considering a synthetic Su-Schrieffer-Heeger lattice with all-to-all nonlocal interactions. We find…
We characterize several phases of gapped spin systems by local order parameters defined by quantized Berry phases. This characterization is topologically stable against any small perturbation as long as the energy gap remains finite. The…
We broaden the scope of quantum field theory by introducing a general class of discrete gauge theories that realize either topological order or fracton behavior across dimensions. We start from translation-invariant systems endowed with…
The combination of topology and quantum criticality can give rise to an exotic mix of counterintuitive effects. Here, we show that unexpected topological properties take place in a paradigmatic strongly-correlated Hamiltonian: the 1D…
Superconductors can be classified as topological or not based on whether time-reversal symmetry (TRS), chiral symmetry, and particle-hole symmetry are preserved or not. Further, topological superconductors can also be classified as chiral…
The topology of the non-adiabatic parameter space bundle is discussed for evolution of exact cyclic state vectors in Berry's original example of split angular momentum eigenstates. It turns out that the change in topology occurs at a…
We use entanglement entropy signatures to establish non-Abelian topological order in projected Chern-insulator wavefunctions. The simplest instance is obtained by Gutzwiller projecting a filled band with Chern number C=2, whose wavefunction…
A prominent example of a topologically ordered system is Kitaev's quantum double model $\mathcal{D}(G)$ for finite groups $G$ (which in particular includes $G = \mathbb{Z}_2$, the toric code). We will look at these models from the point of…
The study of topological band insulators has revealed fascinating phases characterized by band topology indices and anomalous boundary modes protected by global symmetries. In strongly correlated systems, where the traditional notion of…
We present a constructive method utilizing the Cartan decomposition to characterize topological properties and their connection to two-qubit quantum entanglement, in the framework of the tenfold classification and Wootters' concurrence.…
As is well known, coordinates of D-branes are described by NxN matrices. From generic non-commuting matrices, it is difficult to extract physics, for example, the shape of the distribution of positions of D-branes. To overcome this problem,…
Second-order topological insulators (SOTIs) are the topological phases of matter in d dimensions that manifest (d-2)-dimensional localized modes at the intersection of the edges. We show that SOTIs can be designed via stacked Chern…
We first study the importance of the sign of the Berry curvature in the Euler characteristic of the two-dimensional topological material with two bands. Then we report an observation of a character of the topological transition as a…
Topological phases of matter lie at the heart of physics, connecting elegant mathematical principles to real materials that are believed to shape future electronic and quantum computing technologies. To date, studies in this discipline have…