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 …

The Lieb-Schultz-Mattis (LSM) theorem provides a general constraint on quantum many-
body systems and plays a significant role in the Haldane gap phenomena and topological …

Topologically ordered phases in 2+ 1 dimensions are generally characterized by three
mutually related features: fractionalized (anyonic) excitations, topological entanglement …

Abstract Lieb-Schultz-Mattis (LSM) theorems impose non-perturbative constraints on the
zero-temperature phase diagrams of quantum lattice Hamiltonians (always assumed to be …

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 …

We discuss quantum many-body systems with lattice translation and discrete on-site
symmetries. We point out that, under a boundary condition twisted by a symmetry operation …

The index theorems relate the gauge field and metric on a manifold to the solution of the
Dirac equation on it. In the standard approach, the Dirac operator must be massless to make …

The Lieb-Schultz-Mattis (LSM) theorem states that a spin system with translation and spin
rotation symmetry and half-integer spin per unit cell does not admit a gapped symmetric …

In the past few decades, tremendous efforts have been made toward understanding the
exotic physics emerging from competition between various ordering tendencies in strongly …