A Duality Between U(1) Haah Code and 3D Smectic A Phase

Fractonic gauge theory of smectics

Motivated by striped correlated quantum matter, and the recently developed duality between elasticity of a two-dimensional (2D) crystal and a gauge theory, we derive a dual coupled U(1) vector gauge theory for a two-dimensional (2D) quantum smectic, where the disclination is mapped onto the fractonic charge, that we demonstrate can only move transversely to smectic layers. This smectic gauge theory dual also emerges from a gauge dual of a quantum crystal after a Higgs transition corresponding to a single flavor of its dipole condensation, an anisotropic quantum melting via dislocation prolifer…

Fracton-elasticity duality of two-dimensional superfluid vortex crystals: defect interactions and quantum melting

Employing the fracton-elastic duality, we develop a low-energy effective theory of a zero-temperature vortex crystal in a two-dimensional bosonic superfluid which naturally incorporates crystalline topological defects. We extract static interactions between these defects and investigate several continuous quantum transitions triggered by the Higgs condensation of vortex vacancies/interstitials and dislocations. We propose that the quantum melting of the vortex crystal towards the hexatic or smectic phase may occur via a pair of continuous transitions separated by an intermediate vortex superso…

Dual gauge field theory of quantum liquid crystals in two dimensions

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 and an isotropic superfluid: quantum nematics and smectics. It is based on an Abelian-Higgs-type duality mapping of phonons onto gauge bosons ("stress photons"), which encode for the capacity of the crystal to propagate stresses. Dislocations and disclinations, the topological defects of the crystal, are sources for the gauge fields and the melting…

Fracton物质

Fracton Matter

本文回顾了fracton领域，展示了对称张量与耦合矢量规范理论如何从二维量子晶体弹性中涌现，并通过fracton-弹性对偶性与广义Higgs机制描述量子熔化相变及fracton相。