Symmetry protected topological (SPT) phases are gapped short-range-entangled quantum
phases with a symmetry G. They can all be smoothly connected to the same trivial product …

Quantum many-body systems divide into a variety of phases with very different physical
properties. The questions of what kinds of phases exist and how to identify them seem hard …

We show that the Haldane phase of S= 1 chains is characterized by a double degeneracy of
the entanglement spectrum. The degeneracy is protected by a set of symmetries (either the …

In this paper we show how the classification of topological phases in insulators and
superconductors is changed by interactions, in the case of one-dimensional systems. We …

We discuss the characterization and stability of the Haldane phase in integer spin chains on
the basis of simple, physical arguments. We find that an odd-S Haldane phase is a …

The effect of interactions on topological insulators and superconductors remains, to a large
extent, an open problem. Here, we describe a framework for classifying phases of one …

We propose a realization of higher-order topological phases in a spring-mass model with a
breathing kagome structure. To demonstrate the existence of the higher-order topological …

We propose the ZQ Berry phase as a topological invariant for higher-order symmetry-
protected topological (HOSPT) phases for two-and three-dimensional systems. It is …

Waveguide QED has emerged as a powerful analog quantum simulator due to the
possibility of mediating versatile spin-spin interactions with tunable sign, range, and even …

Beyond the well-known topological band theory for single-particle systems, it is a great
challenge to characterize the topological nature of interacting multiparticle quantum …