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 …

In principle, a complex assembly of strongly interacting electrons can self-organize into a
wide variety of collective states, but relatively few such states have been identified in …

We present a unifying framework to study physical systems which exhibit topological
quantum order (TQO). The major guiding principle behind our approach is that of …

We present an overview of recent developments in species-imbalanced ('polarized')
Feshbach-resonant Fermi gases. We summarize the current status of thermodynamics of …

We develop a low-energy model of an unidirectional Larkin-Ovchinnikov (LO) state.
Because the underlying rotational and translational symmetries are broken spontaneously …

We present a gauge theory formulation of a two-dimensional quantum smectic and its
relatives, motivated by their realizations in correlated quantum matter. The description gives …

Motivated by a realization of imbalanced Feshbach-resonant atomic Fermi gases, we
formulate a low-energy theory of the Fulde-Ferrell and the Larkin-Ovchinnikov (LO) states …

Motivated by variety of realizations of the compact Lifshitz model, I predict and explore
properties of its three phases, study its phase transitions and derive its fractonic gauge dual …

We extend Elitzur's theorem to systems with symmetries intermediate between global and
local. In general, our theorem formalizes the idea of dimensional reduction. We apply the …

The topological physics of quantum Hall states is efficiently encoded in purely topological
quantum field theories of the Chern-Simons type. The reliable inclusion of low-energy …