Long-range entanglement—the backbone of topologically ordered states—cannot be
created in finite time using local unitary circuits, or, equivalently, adiabatic state preparation …

We present a systematic recipe for generating and classifying duality transformations in one-
dimensional quantum lattice systems. Our construction emphasizes the role of global …

Symmetry is usually defined via transformations described by a (higher) group. But a
symmetry really corresponds to an algebra of local symmetric operators, which directly …

It has been a long-standing open problem to construct a general framework for relating the
spectra of dual theories to each other. Here, we solve this problem for the case of one …

We show that the path integral of conformal field theories in D dimensions (CFT D) can be
constructed by solving for eigenstates of a renormalization group (RG) operator following …

Despite growing interest in beyond-group symmetries in quantum condensed matter
systems, there are relatively few microscopic lattice models explicitly realizing these …

Projective symmetries are ubiquitous in quantum lattice models and can be leveraged to
constrain their phase diagram and entanglement structure. In this paper, we investigate the …

In this work, we analyze the macroscopic observables in the 1+ 1 D gapped phases with
Abelian onsite symmetries and show that the spacetime observables for each gapped phase …

The bulk-boundary correspondence is a hallmark feature of topological phases of matter.
Nonetheless, our understanding of the correspondence remains incomplete for phases with …

Cluster states are crucial resources for measurement-based quantum computation (MBQC).
It exhibits symmetry-protected topological (SPT) order, thus also playing a crucial role in …