This is an introductory review of the physics of topological quantum matter with cold atoms.
Topological quantum phases, originally discovered and investigated in condensed matter …

Supersolid states simultaneously feature properties typically associated with a solid and with
a superfluid. Like a solid, they possess crystalline order, manifesting as a periodic …

We study a one-dimensional ladder of two coupled XXZ spin chains and identify several
distinct gapless symmetry-enriched critical phases. These have the same unbroken …

We introduce topological invariants for gapless systems and study the associated boundary
phenomena. More generally, the symmetry properties of the low-energy conformal field …

Topology in quantum matter is typically associated with gapped phases. For example, in
symmetry protected topological (SPT) phases, the bulk energy gap localizes edge modes …

We gauge the fermion parity symmetry of the Kitaev chain. While the bulk of the model
becomes an Ising chain of gauge-invariant spins in a tilted field, near the boundaries the …

We introduce a systematic construction of a gapless symmetry-protected topological phase
in one dimension by “decorating” the domain walls of Luttinger liquids. The resulting strongly …

We revisit the low-energy physics of one-dimensional spinless fermion liquids, showing that
with sufficiently strong interactions the conventional Luttinger liquid can give way to a strong …

We study how symmetry can enrich strong-randomness quantum critical points and phases,
and lead to robust topological edge modes coexisting with critical bulk fluctuations. These …

We study a three-leg spin-1/2 ladder with geometrically frustrated interleg interactions. We
call this model an anisotropic triangular-strip (ATS) model. We numerically and field …