We present a self-contained review of the theory of dislocation-mediated quantum melting at
zero temperature in two spatial dimensions. The theory describes the liquid-crystalline …

Exotic physics could emerge from interplay between geometry and correlation. In fractional
quantum Hall (FQH) states, novel collective excitations called chiral graviton modes (CGMs) …

Fractional Chern insulators realize the remarkable physics of the fractional quantum Hall
effect (FQHE) in crystalline systems with Chern bands. The lowest Landau level (LLL) is …

Geometric fluctuations of the density mode in a fractional quantum Hall (FQH) state can give
rise to a nematic FQH phase, a topological state with a spontaneously broken rotational …

We present an effective field theory approach to the fracton phases. The approach is based
on the notion of a multipole algebra. It is an extension of space (time) symmetries of a …

We present a bimetric low-energy effective theory of fractional quantum Hall (FQH) states
that describes the topological properties and a gapped collective excitation, known as the …

We analyze the “higher rank” gauge theories that capture some of the phenomenology of the
fracton order. It is shown that these theories lose gauge invariance when an arbitrarily weak …

Abstract Topological phases in (2+ 1)-dimensions are frequently equipped with global
symmetries, like conjugation, bilayer or electric–magnetic duality, that relabel anyons …

The quantum Hall effect is a prototypical realization of a topological state of matter. It
emerges from a subtle interplay between topology, interactions and disorder,,,,,,,–. The …

We derive an effective field theory for the isotropic-nematic quantum phase transition of
fractional quantum Hall states. We demonstrate that for a system with an isotropic …