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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 a unified treatment of phonons and topological defects, respectively encoded in a pair of coupled gauge fields and corresponding charges. The charges exhibit subdimensional constrained quantum dynamics and anomalously slow highly anisotropic diffusion of disclinations inside a smectic. This approach gives a transparent description of a multi-stage quantum melting transition of a two-dimensional commensurate crystal (through an incommensurate crystal - a supersolid) into a quantum smectic, that subsequently melts into a quantum nematic and isotropic superfluids, all in terms of a sequence of Higgs transitions.
Nematic phases, breaking spontaneously rotational symmetry, provide for ubiquitously observed states of matter in both classical and quantum systems. These nematic states may be further classified by their $N$--fold rotational invariance described by
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 phases with spatial symmetries in between a quantum crystalline solid
The dislocation-mediated quantum melting of solids into quantum liquid crystals is extended from two to three spatial dimensions, using a generalization of boson-vortex or Abelian-Higgs duality. Dislocations are now Burgers-vector-valued strings that
We study chiral phase transition and confinement of matter fields in (2+1)-dimensional U(1) gauge theory of massless Dirac fermions and scalar bosons. The vanishing scalar boson mass, $r=0$, defines a quantum critical point between the Higgs phase an
We demonstrate several explicit duality mappings between elasticity of two-dimensional crystals and fracton tensor gauge theories, expanding on recent works by two of the present authors. We begin by dualizing the quantum elasticity theory of an ordi