Spectroscopic fingerprints of gapless type-II fracton phases
Fracton phases feature elementary excitations with fractionalized mobility and are exciting interest from multiple areas of theoretical physics. However, the most exotic type-II fracton phases, like the Haah codes, currently have no known experimental diagnostics. Here, we explain how type-II fracton phases with gapless gauge modes, such as the U(1) Haah code, may be identified experimentally. Our analysis makes use of the multipole gauge theory description of type-II fracton phases, which exhibits ultraviolet-infrared (UV-IR) mixing. We show that neutron scattering experiments on gapless type-II fracton phases should generically exhibit exotic pinch points in the structure factor, with distinctive anisotropic contours as a direct consequence of UV-IR mixing. Furthermore, this characteristic pinch point structure provides a clean diagnostic of type-II fracton phases. We also identify distinctive signatures of the (3 + 1)-D U(1) Haah code in the low-temperature specific heat.