We analyze lattice Hamiltonian systems whose global symmetries have't Hooft anomalies.
As is common in the study of anomalies, they are probed by coupling the system to classical …

We discuss the exact non-invertible Kramers-Wannier symmetry of 1+ 1d lattice models on a
tensor product Hilbert space of qubits. This symmetry is associated with a topological defect …

A system with charge conservation and lattice translation symmetry has a well-defined filling
ν, which is a real number representing the average charge per unit cell. We show that if ν is …

It is known that the classical O (N) model in dimension d> 3 at its bulk critical point admits
three boundary universality classes: the ordinary, the extra-ordinary and the special. For the …

We show how to define a quantized many-body charge polarization 𝒫→ for (2+ 1) D
topological phases of matter, even in the presence of nonzero Chern number and magnetic …

We propose a new type of quantum liquids, dubbed Stiefel liquids, based on (2+ 1)-
dimensional nonlinear sigma models on target space SO (N)/SO (4), supplemented with …

While free fermion topological crystalline insulators have been largely classified, the
analogous problem in the strongly interacting case has been only partially solved, and the …

We show that a quantum state in a lattice spin (boson) system must be long-range entangled
if it has nonzero lattice momentum, ie, if it is an eigenstate of the translation symmetry with …

Symmetric mass generation (SMG) is a mechanism to give gapless fermions a mass gap by
nonperturbative interactions without generating any fermion bilinear condensation. The …

Quantum entanglement measures of many-body states have been increasingly useful to
characterize phases of matter. Here we explore a surprising connection between mixed …