Related papers: Genus-protected higher-order topological phases
We argue that symmetry-broken phases proximate in phase space to symmetry-protected topological phases can exhibit dynamical signatures of topological physics. This dynamical, symmetry-protected "topological" regime is characterized by…
We study the bulk-boundary correspondence for topological crystalline phases, where the crystalline symmetry is an order-two (anti)symmetry, unitary or antiunitary. We obtain a formulation of the bulk-boundary correspondence in terms of a…
We demonstrate the existence of topologically nontrivial phase in a one-dimensional fermionic lattice system subjected to synthetic gauge fields, which is beyond the standard Altland-Zirnbauer classification of topological insulators. The…
The concept of topological phases has been generalized to higher-order topological insulators and superconductors with novel boundary states on corners or hinges. Meanwhile, recent experimental advances in controlling dissipation (such as…
Topological physics opens a door towards flexible routing and resilient localization of waves of various nature. Recently proposed higher-order topological insulators provide advanced control over wave localization in the structures of…
We theoretically demonstrate that interacting symmetry-protected topological (SPT) phases can be realized with ultracold spinful bosonic atoms loaded on the lattices which have a flat band at the bottom of the band structure. Ground states…
In recent years, the role of crystal symmetries in enriching the variety of TIs have been actively investigated. Higher-order TIs are a new type of topological crystalline insulators that exhibit gapless boundary states whose dimensionality…
Crystalline symmetries give rise to topological invariants that can distinguish quantum phases of matter. Understanding these in strongly interacting systems is an ongoing research direction requiring non-perturbative methods. Recent…
Non-Abelian topological charges (NATCs), characterized by their noncommutative algebra, offer a framework for describing multigap topological phases beyond conventional Abelian invariants. While higher-order topological phases (HOTPs) host…
We study a two dimensional super-lattice Bose-Hubbard model with alternating hoppings in the limit of strong on-site interactions. We evaluate the phase diagram of the model around half-filling using the density matrix renormalization group…
Symmetry-protected topological (SPT) phases are many-body quantum states that are topologically nontrivial as long as the relevant symmetries are unbroken. In this work we show that SPT phases are also well defined for average symmetries,…
Topological phases are often characterized by special edge states confined near the boundaries by an energy gap in the bulk. On raising temperature, these edge states are lost in a clean system due to mobile thermal excitations. Recently…
We classify a number of symmetry protected phases using Freed-Hopkins' homotopy theoretic classification. Along the way we compute the low-dimensional homotopy groups of a number of novel cobordism spectra.
Topological insulators~(TIs) are a new class of materials that resemble ordinary band insulators in terms of a bulk band gap but exhibit protected metallic states on their boundaries. In this modern direction, higher-order TIs~(HOTIs) are a…
The concepts of topology have a profound impact on physics research spanning the fields of condensed matter, photonics and acoustics and predicting topological states that provide unprecedented versatility in routing and control of waves of…
Symmetry and topology are essential principles in topological physics. Recently, the idea of sub-symmetry-protected topology -- where some of the original symmetries are broken while a remaining subset, called sub-symmetries, continues to…
We show that topology can protect exponentially localized, zero energy edge modes at critical points between one-dimensional symmetry protected topological phases. This is possible even without gapped degrees of freedom in the bulk ---in…
Over the last few years, crystalline topology has been used in photonic crystals to realize edge- and corner-localized states that enhance light-matter interactions for potential device applications. However, the band-theoretic approaches…
We make a systematic study of symmetry-protected topological gapped phases of quantum spin chains in the presence of the frieze space groups in one dimension using matrix product states. Here, the spatial symmetries of the one-dimensional…
Robust states emerging at the boundary of a system constitute a hallmark for topological band structures. Other than in closed systems, topologically protected states can occur even in systems with a trivial band structure, if exposed to…