Topological materials have become the focus of intense research in recent years, since they
exhibit fundamentally new physical phenomena with potential applications for novel devices …

We examine the interplay of symmetry and topological order in 2+ 1-dimensional topological
quantum phases of matter. We present a precise definition of the topological symmetry …

The Lieb-Schultz-Mattis theorem and its higher-dimensional generalizations by Oshikawa
and Hastings require that translationally invariant 2D spin systems with a half-integer spin …

Symmetry fractionalization describes the fascinating phenomena that excitations in a 2D
topological system can transform under symmetry in a fractional way. For example in …

A bstract We study a 3d lattice gauge theory with gauge group U (1) N− 1⋊ SN, which is
obtained by gauging the SN global symmetry of a pure U (1) N− 1 gauge theory, and we call …

A bstract We consider the SU (N) Yang-Mills theory, whose topological sectors are restricted
to the instanton number with integer multiples of p. We can formulate such a quantum field …

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 …

The Lieb-Schultz-Mattis (LSM) theorem dictates that emergent low-energy states from a
lattice model cannot be a trivial symmetric insulator if the filling per unit cell is not integral …

The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack
of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is …

Abstract Topological phases in (2+ 1)-dimensions are frequently equipped with global
symmetries, like conjugation, bilayer or electric–magnetic duality, that relabel anyons …