This research proposal presents a comprehensive framework to understand emergent hydrodynamics from quantum criticality in higher-dimensional lattice systems. It combines effective field theory, generalized hydrodynamics, and quantum simulation protocols to investigate macroscopic hydrodynamic behavior emerging from microscopic quantum dynamics near critical points.
Key findings
Develops a theoretical methodology for extracting hydrodynamic variables from lattice models.
Proposes a classification scheme for universality classes of critical hydrodynamics.
Derives predictions for transport coefficients, dynamic structure factors, and critical exponents.
Limitations & open questions
Most exactly solvable models are restricted to one dimension.
Dimensional crossover from 1D to 2D and 3D remains poorly understood.