We consider three topics, all concerning the confluence of dynamics, disorder, and interactions in low-dimensional quantum many-body systems of interest for the potential manipulation of quantum matter.

Particle fractionalization is believed to orchestrate the physics of many strongly correlated systems, yet its direct experimental detection remains a challenge. We propose a measurement for an ultracold matter system, in which correlations in initially decoupled 1D chains are imprinted via quantum quench upon two-dimensional Dirac fermions. Coupling fractionalized initial states launches relativistic "fractionalization waves'' along the chains, while coupling noninteracting chains induces perpendicular dispersion. These could be easily distinguished in an ultracold gas experiment.

As a potential window on transitions out of the ergodic phase of weakly disordered, quasi-one-dimensional fermion systems, we study dephasing due to a diffusive noise bath generated by inelastic scattering due to short-ranged interactions. We calculate the dephasing of weak localization perturbatively through second order in the bath coupling and discover a failure of the self-consistent Born approximation. We also consider a many-channel quantum wire where short-ranged, spin-exchange interactions coexist with screened Coulomb interactions. We calculate the dephasing rate, treating the short-ranged interaction perturbatively and the Coulomb interaction exactly, giving the first controlled calculation of quasi-1D dephasing due to diffusive noise. Our results are relevant to the search for precursors to the many-body localization transition. They also link dephasing to the enhancement of the spin-triplet interaction near a metal-insulator transition, providing for the amplification of dephasing at low temperatures in spin SU(2)-symmetric quantum wires.

The physics of massless, 2D Dirac fermions with a spatially modulated Dirac cone could have important applications in low-dimensional superconductivity and other Dirac materials. This is mathematically identical to a theory of massless fermions on a certain class of curved spacetime manifolds. We study these manifolds, which are dominated by curvature singularities, and find that isotropic and nematic fluctuations have profound yet different effects on the spacetime geometry. We present analytical results on geodesic geometry, give some exact solutions for some highly-symmetric toy models, and speculate about the role of induced one-dimensionality for such bound orbits in the physics of 2D dirty d-wave superconductivity.