Fracton hydrodynamics

Abstract

We introduce new classes of hydrodynamic theories inspired by the recently discovered fracton phases of quantum matter. Fracton phases are characterized by elementary excitations (fractons) with restricted mobility. The hydrodynamic theories we introduce describe thermalization in systems with fractonlike mobility constraints, including fluids where charge and dipole moment are both locally conserved, and fluids where charge is conserved along every line or plane of a lattice. Each of these fluids is subdiffusive and constitutes a new universality class of hydrodynamic behavior. There are infinitely many such classes, each with distinct subdiffusive exponents, all of which are captured by our formalism. Our framework naturally explains recent results on dynamics with constrained quantum circuits, as well as recent experiments with ultracold atoms in tilted optical lattices. We identify crisp experimental signatures of these novel hydrodynamics and explain how they may be realized in near term ultracold atom experiments.

Subdiffusion in strongly tilted lattice systems

“…which leads to the relaxation rate 1/τ ∝ k 4 . Similar subdiffusion equation has also been found recently in fracton models [22] and specific circuit model with dipole moment conservation [19]. Our analysis here can be directly applied to analyze the strongly tilt limit of the tilted Fermi Hubbard model realized in Ref.…”

“…Note that this is different from the low-dimensional models [15][16][17][18] which show transitions between ergodic and nonergodic phases. Very recently, subdiffusion behavior is also observed in a specific circuit model that conserves the dipole momentum [19], where both symmetries are imposed from the beginning [20] and in more sophisticated fracton models [21,22]. To further support our analysis, we construct a solvable model by adding strong tilted potential to the quadratically coupled Sachdev-Ye-Kitaev model (SYK) [23][24][25][26].…”

Exotic $U(1)$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory

“…Most of the discussion in [3] focused on the XY-plaquette model [7], whose 2+1-dimensional continuum Lagrangian is [7][8][9][10][11][12][13] (related Lagrangians appeared in [14][15][16])…”

“…Certain aspects of the gauge theory of A have been discussed in [8,9,12,[17][18][19] (see [10,11,13,15,16,[20][21][22][23][24][25][26][27][28][29][30][31] for related tensor gauge theories). The gauge theory of is related to gauge theories discussed in [8,12].…”

Magnetophonons & type-B Goldstones from hydrodynamics to holography

“…3 More exotic subdiffusive modes (e.g. ω = −i D k 4 ) can arise within the hydrodynamic theory of fractons [27].…”