相关论文: Boundary conformal field theory and symmetry prote…
Quantum phase transitions out of a symmetry-protected topological (SPT) phase in (1+1) dimensions into an adjacent, topologically distinct SPT phase protected by the same symmetry or a trivial gapped phase, are typically described by a…
Symmetry topological field theory (SymTFT) gives a holographic correspondence between systems with a global symmetry and a higher-dimensional topological field theory. In this framework, classification of gapped phases of matter in…
We study gapless phases in (3+1)d in the presence of 1-form and non-invertible duality symmetries. Using the Symmetry Topological Field Theory (SymTFT) approach, we classify the gapless symmetry-protected (gSPT) phases in these setups, with…
It is well known that (1+1)-D bosonic symmetry-protected topological (SPT) phases with symmetry group $G$ can be identified by the projective representation of the symmetry at the edge. Here, we generalize this result to higher dimensions.…
Twisting symmetries provides an efficient method to diagnose symmetry-protected topological (SPT) phases. In this paper, edge theories of (2+1)-dimensional topological phases protected by reflection as well as other symmetries are studied…
Symmetry protected topological (SPT) phases are gapped quantum phases which host symmetry-protected gapless edge excitations. On the other hand, the edge states can be gapped by spontaneously breaking symmetry. We show that topological…
Gapless quantum phases can become distinct when internal symmetries are enforced, in analogy with gapped symmetry-protected topological (SPT) phases. However, this distinction does not always lead to protected edge modes, raising the…
Symmetry-protected topological (SPT) phases are short-range entangled quantum states characterized by anomalous edge behavior, a manifestation of the bulk-boundary correspondence for topological phases. Moreover, the Li-Haldane conjecture…
Symmetry protected topological (SPT) phases with unusual edge excitations can emerge in strongly interacting bosonic systems and are classified in terms of the cohomology of their symmetry groups. Here we provide a physical picture that…
Symmetry topological field theory (SymTFT), or topological holography, posits a correspondence between symmetries in a $d$-dimensional theory and topological order in a $(d+1)$-dimensional theory. In this work, we extend this framework to…
We introduce exactly solvable gapless quantum systems in $d$ dimensions that support symmetry protected topological (SPT) edge modes. Our construction leads to long-range entangled, critical points or phases that can be interpreted as…
Symmetry protected topological (SPT) states have boundary 't Hooft anomalies that obstruct an effective boundary theory realized in its own dimension with UV completion and an on-site $G$-symmetry. In this work, yet we show that a certain…
We explore 1+1 dimensional (1+1D) gapped phases in systems with non-invertible symmetries, focusing on symmetry-protected topological (SPT) phases (defined as gapped phases with non-degenerate ground states), as well as SPT orders (defined…
We use the Symmetry Topological Field Theory (SymTFT) to systematically characterize gapped phases in 2+1 dimensions with categorical symmetries. The SymTFTs that we consider are (3+1)d Dijkgraaf-Witten (DW) theories for finite groups $G$,…
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 state if we break the symmetry. The Haldane phase of spin-1 chain…
Symmetry protected topological (SPT) states are bulk gapped states with gapless edge excitations protected by certain symmetries. The SPT phases in free fermion systems, like topological insulators, can be classified by the K-theory.…
Fusion category symmetries are finite symmetries in 1+1 dimensions described by unitary fusion categories. We classify 1+1d time-reversal invariant bosonic symmetry protected topological (SPT) phases with fusion category symmetry by using…
In this work we study gapped boundary states of $\mathbb{Z}_N$ bosonic symmetry-protected topological (SPT) phases in 4+1d, which are characterized by mixed $\mathbb{Z}_N$-gravity response, and the closely related phases protected by $C_N$…
Symmetry-protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry $G$, which can all be smoothly connected to the trivial product states if we break the symmetry. It has been shown that a large…
We study glide protected topological (GSPT) phases of interacting bosons and fermions in three spatial dimensions certain on-site symmetries. They are crystalline SPT phases, which are distinguished from a trivial product state only in the…