相关论文: Bosonization and Anomaly Indicators of (2+1)-D Fer…

We derive a framework to apply topological quantum chemistry in systems subject to magnetic flux. We start by deriving the action of spatial symmetry operators in a uniform magnetic field, which extends Zak's magnetic translation groups to…

We revisit 't Hooft anomalies in (1+1)$d$ non-spin quantum field theory, starting from the consistency and locality conditions, and find that consistent U(1) and gravitational anomalies cannot always be canceled by properly quantized…

We define and compute many-body topological invariants of interacting fermionic symmetry-protected topological phases, protected by an orientation-reversing symmetry, such as time-reversal or reflection symmetry. The topological invariants…

For each $\alpha \in \{0,1,-1 \}$, we count diagonally and antidiagonally symmetric alternating sign matrices (DASASMs) of fixed odd order with a maximal number of $\alpha$'s along the diagonal and the antidiagonal, as well as DASASMs of…

We prove that the boundaries of all non-trivial 1+1 dimensional intrinsically fermionic symmetry-protected-topological phases, protected by finite on-site symmetries (unitary or anti-unitary), are supersymmetric quantum mechanical systems.…

In this paper, we present a construction toward a new type of TQFTs at the crossroads of low-dimensional topology, algebraic geometry, physics, and homotopy theory. It assigns TMF-modules to closed 3-manifolds and maps of TMF-modules to…

We point out that fermionic unitary operators which anticommute among themselves appear in various situations in quantum field theories with anomalies in the Hamiltonian formalism. To illustrate, we give multiple derivations of the fact…

We investigate symmetry-preserving gapped boundary of (2+1)D topological phases with global symmetry, which can be either bosonic or fermionic. We develop a general algebraic description for gapped boundary condition for symmetry-enriched…

We review the dimensional reduction procedure in the group cohomology classification of bosonic SPT phases with finite abelian unitary symmetry group. We then extend this to include general reductions of arbitrary dimensions and also extend…

In [BK], it is shown that the Turaev-Viro invariants defined for a spherical fusion category $\mathcal{A}$ extends to invariants of 3-manifolds with corners. In [Kir], an equivalent formulation for the 2-1 part of the theory (2-manifolds…

A large class of gapped phases of matter can be described by topological finite group gauge theories. In this paper we show how such gauge theories possess a higher-group global symmetry, which we study in detail. We derive the $d$-group…

Supersymmetry, originally proposed in particle physics, refers to a dual relation that connects fermionic and bosonic degrees of freedom in a system. Recently, there has been considerable interest in applying the idea of supersymmetry to…

Symmetry protected topological (SPT) phases are well understood in the context of free fermions and in the context of interacting but essentially bosonic models. Recently it has been realized that intrinsically fermionic SPTs exist which…

We construct a dual bosonized description of a massless Majorana fermion in $(2+1)d$. In contrast to Dirac fermions, for which a bosonized description can be constructed using a flux attachment procedure, neutral Majorana fermions call for…

We study bosonic symmetry-protected topological (SPT) phases in (2+1) dimensions with symmetry $G = G_{\text{space}}\times K$, where $G_{\text{space}}$ is a general wallpaper group and $K=\text{U}(1),\mathbb{Z}_N, \text{SO}(3)$ is an…

We study topological defect lines (TDLs) in two-dimensional $\mathbb Z_N$-parafermoinic CFTs. Different from the bosonic case, in the 2d parafermionic CFTs, there exist parafermionic defect operators that can live on the TDLs and satisfy…

This paper generalizes two facts about oriented 3d TFTs to the unoriented case. On one hand, it is known that oriented 3d TFTs having a topological boundary condition admit a state-sum construction known as the Turaev-Viro construction.…

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…

The phases with spontaneously broken symmetries corresponding to antiferromagnetic and d-wave superconducting order in the two-dimensional t-t'-Hubbard model are investigated by means of the functional renormalization group. The…

Strange correlators are useful tools for diagnosing symmetry-protected topological states from their bulk wave functions. We study strange correlators for one-dimensional fermionic symmetry-protected topological states using fixed-point…