Related papers: Sorting topological stabilizer models in three dim…
The homotopy theory of topological defects in ordered media fails to completely characterize systems with broken translational symmetry. We argue that the problem can be understood in terms of the lack of rotational Goldstone modes in such…
Entanglement entropy provides a powerful characterization of two-dimensional gapped topological phases of quantum matter, intimately tied to their description by topological quantum field theories (TQFTs). Fracton topological orders are…
Topological insulators are described by topological invariants that can be computed by integrals over momentum space, but also as traces over local, real-space topological markers. These markers are useful to detect topological insulating…
We introduce the notion of topological electronic states on random lattices in non-integer dimensions. By considering a class $D$ model on critical percolation clusters embedded in two dimensions, we demonstrate that these topological…
Higher-order topological insulators are established as topological crystalline insulators protected by crystalline symmetries. One celebrated example is the second-order topological insulator in three dimensions that hosts chiral hinge…
We develop a theoretical framework for the classification and construction of symmetry protected topological (SPT) phases, which are a special class of zero-temperature phases of strongly interacting gapped quantum many-body systems that…
We provide topological classification of possible phases with the symmetry of the planar phase of superfluid $^3$He. Compared to the B-phase (class DIII in classification of Altland and Zirnbauer), it has an additional symmetry, which…
We point out the existence of an arithmetical symmetry for the commutant of the modular matrices S and T. This symmetry holds for all affine simple Lie algebras at all levels and implies the equality of certain coefficients in any modular…
We focus on 4D $\mathcal{N}=2$ string vacua described both by perturbative Heterotic theory and by Type IIA theory; a Calabi--Yau three-fold $X_{\rm IIA}$ in the Type IIA language is further assumed to have a regular K3-fibration. It is…
We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. We show that all these symmetry protected topological states can be…
We address the problem of identifying a 2+1d topologically ordered phase using measurements on the ground-state wavefunction. For non-chiral topological order, we describe a series of bulk multipartite entanglement measures that extract the…
Symmetry Protected Topological (SPT) phases are a minimal generalization of the concept of topological insulators to interacting systems. In this paper we describe the classification and properties of such phases for three dimensional(3D)…
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…
We define and compute many-body topological invariants of interacting fermionic symmetry-protected topological phases, protected by an orientation-reversing symmetry, such as time-reversal or reflection symmetry. The topological invariants…
The idea of modular invariance provides a novel explanation of flavour mixing. Within the context of finite modular symmetries $\Gamma_N$ and for a given element $\gamma \in \Gamma_N$, we present an algorithm for finding stabilisers…
Fracton order is a new kind of quantum order characterized by topological excitations that exhibit remarkable mobility restrictions and a robust ground state degeneracy (GSD) which can increase exponentially with system size. In this paper,…
Recent realizations of exotic topological states in condensed matter and cold atoms have advanced the exploration for topological characteristics, such as invariant topological orders and band inversion. Here we construct a 1D optical…
At the heart of the study of topological insulators lies a fundamental dichotomy: topological invariants are defined in infinite systems, but surface states as their main footprint only exist in finite systems. In the slab geometry, namely…
We discuss different properties and the ability of several topological invariants based on position operators to identify phase transitions, and compare with more accurate methods, like crossing of excited energy levels and jumps in Berry…
Recent progress toward classifying low-dimensional chaos measured from time series data is described. This classification theory assigns a template to the time series once the time series is embedded in three dimensions. The template…