相关论文: Mirror anomaly in fermionic topological orders

Two-dimensional mirror symmetry enriched topological (SET) orders can be studied using the folding approach: it can be folded along the mirror axis and turned into a bilayer system on which the mirror symmetry acts as a $\mathbb Z_2$…

We derive a series of quantitative bulk-boundary correspondences for 3D bosonic and fermionic symmetry-protected topological (SPT) phases under the assumption that the surface is gapped, symmetric and topologically ordered, i.e., a…

We develop a folding approach to study two-dimensional symmetry-enriched topological (SET) phases with the mirror reflection symmetry. Our folding approach significantly transforms the mirror SETs, such that their properties can be…

We develop a theory of anomalies of fermionic topological phases of matter in (2+1)D with a general fermionic symmetry group $G_f$. In general, $G_f$ can be a non-trivial central extension of the bosonic symmetry group $G_b$ by fermion…

We study anomalies in time-reversal ($\mathbb{Z}_2^T$) and $U(1)$ symmetric topological orders. In this context, an anomalous topological order is one that cannot be realized in a strictly $(2+1)$-D system but can be realized on the surface…

The interplay between symmetry and topological properties plays a very important role in modern physics. In the past decade, the concept of symmetry-enriched topological (SET) phases was proposed and their classifications have been…

We provide a mathematical proposal for the anomaly indicators of symmetries of (2+1)-d fermionic topological orders, and work out the consequences of our proposal in several nontrivial examples. Our proposal is an invariant of a super…

Symmetry acting on a (2+1)$D$ topological order can be anomalous in the sense that they possess an obstruction to being realized as a purely (2+1)$D$ on-site symmetry. In this paper, we develop a (3+1)$D$ topological quantum field theory to…

The surface of a three-dimensional topological electron system often hosts symmetry-protected gapless surface states. With the effect of electron interactions, these surface states can be gapped out without symmetry breaking by a surface…

Symmetry-protected topological phases protected by crystalline symmetries and internal symmetries are shown to enjoy a fascinating one-to-one correspondence in classification. Here we investigate the physics content behind the abstract…

The hallmark of a 2 dimensional topologically ordered phase is the existence of deconfined `anyon' excitations that have exotic braiding and exchange statistics, different from those of ordinary bosons or fermions. As opposed to…

In addition to possessing fractional statistics, anyon excitations of a 2D topologically ordered state can realize symmetry in distinct ways , leading to a variety of symmetry enriched topological (SET) phases. While the symmetry…

In a phase with fractional excitations, topological properties are enriched in the presence of global symmetry. In particular, fractional excitations can transform under symmetry in a fractionalized manner, resulting in different Symmetry…

It is well known that two-dimensional fermionic systems with a nonzero Chern number must break the time reversal symmetry, manifested by the appearance of chiral edge modes on an open boundary. Such an incompatibility between topology and…

While the topological classification of insulators, semimetals, and superconductors in terms of nonspatial symmetries is well understood, less is known about topological states protected by crystalline symmetries, such as mirror reflections…

The natural existence of crystalline symmetry in real materials manifests the importance of understanding crystalline symmetry-protected topological (SPT) phases, especially for interacting systems. In this paper, we systematically…

We present microscopic Hamiltonians that gap the Dirac fermions on the surface of topological crystalline insulators (TCIs) protected by reflection symmetry and create symmetry-preserving states with Abelian topological orders. For TCIs…

We investigate (3+1)d topological orders in fermionic systems with an anomalous $\mathbb{Z}_{2N}^{\mathrm{F}}$ symmetry, where its $\mathbb{Z}_2^{\mathrm{F}}$ subgroup is the fermion parity. Such an anomalous symmetry arises as the discrete…

Topological heavy-fermion systems in three dimensions are usually classified as topological insulators or semimetals. Here, we theoretically predict a different type of heavy-fermion system (dubbed exceptional heavy-fermion semimetal) by…

Quantum anomalies, breakdown of classical symmetries by quantum effects, provide a sharp definition of symmetry protected topological phases. In particular, they can diagnose interaction effects on the non-interacting classification of…