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 …

Fractional topological insulators (FTIs) are electronic systems that carry fractionally charged
excitations, conserve charge, and are symmetric to reversal of time. In this review, we …

Coupled-wire constructions use bosonization to analytically tackle the strong interactions
underlying fractional topological states of matter. We give an introduction to this technique …

The major breakthroughs in understanding of topological materials over the past decade
were all triggered by the discovery of the Z2-type topological insulator—a type of material …

Arrays of Rydberg atoms constitute a highly tunable, strongly interacting venue for the
pursuit of exotic states of matter. We develop a strategy for accessing a family of …

We study spinless electrons in a single-channel quantum wire interacting through attractive
interaction, and the quantum Hall states that may be constructed by an array of such wires …

The Lieb-Schultz-Mattis (LSM) theorem and its higher-dimensional generalizations by
Oshikawa and Hastings establish that a translation-invariant lattice model of spin-1 2′ s …

We introduce a two-dimensional electronic insulator that possesses a toric-code topological
order enriched by translation symmetry. This state can be realized from disordering a weak …

The coupled-wire construction provides a useful way to obtain microscopic Hamiltonians for
various two-dimensional topological phases, among which fractional quantum Hall states …

Topological crystalline insulators (TCIs) are nontrivial quantum phases of matter protected
by crystalline (and other) symmetries. They are originally predicted by band theories, so an …