We formulate a family of spin Topological Quantum Field Theories (spin-TQFTs) as fermionic
generalization of bosonic Dijkgraaf–Witten TQFTs. They are obtained by gauging G …

We present a systematic framework to classify symmetry-enriched topological quantum spin
liquids in two spatial dimensions. This framework can deal with all topological quantum spin …

We design a strange correlator for the recently discovered average symmetry-protected
topological (ASPT) phases in $1 d $ and $2 d $. The strange correlator has long-range or …

While free fermion topological crystalline insulators have been largely classified, the
analogous problem in the strongly interacting case has been only partially solved, and the …

The theory of topological phases of matter predicts invariants protected only by crystalline
symmetry, yet it has been unclear how to extract these from microscopic calculations in …

The construction and classification of crystalline symmetry protected topological (SPT)
phases in interacting bosonic and fermionic systems have been intensively studied in the …

Topological crystalline states (TCSs) are short-range entangled states jointly protected by
onsite and crystalline symmetries. Here we present a unified scheme for constructing all …

Topological crystalline superconductors have attracted rapidly rising attention due to the
possibility of higher-order phases, which support Majorana modes on boundaries in d− 2 or …

Motivated by symmetry-protected topological phases (SPTs) with both spatial symmetry (eg,
lattice rotation) and internal symmetry (eg, spin rotation), we propose a class of exotic …

The natural existence of crystalline symmetry in real materials manifests the importance of
understanding crystalline symmetry-protected topological (SPT) phases, especially for …