We construct infinite families of new universality classes of fracton hydrodynamics with momentum conservation, both with multipole conservation laws and/or subsystem symmetry. We explore the effects of broken inversion and/or time-reversal symmetry at the ideal fluid level, along with momentum relaxation. In the case of one-dimensional multipole-conserving models, we write down explicit microscopic Hamiltonian systems realizing these new universality classes. All of these hydrodynamic universality classes exhibit instabilities and will flow to new nonequilibrium fixed points. Such fixed points are predicted to exist in arbitrarily large spatial dimensions.
We investigate the thermodynamics of equilibrium thermal states and their near-equilibrium dynamics in systems with fractonic symmetries in arbitrary curved space. By explicitly gauging the fracton algebra we obtain the geometry and gauge fields that field theories with conserved dipole moment couple to. We use the resultant fracton geometry to show that it is not possible to construct an equilibrium partition function for global thermal states unless part of the fractonic symmetries is spontaneously broken. This leads us to introduce two classes of fracton superfluids with conserved energy and momentum, namely p p -wave and s s -wave fracton superfluids. The latter phase is an Aristotelian superfluid at ideal order but with a velocity constraint and can be split into two separate regimes: The U(1) fracton superfluid and the pinned s s -wave superfluid regimes. For each of these classes and regimes we formulate a hydrodynamic expansion and study the resultant modes. We find distinctive features of each of these phases and regimes at ideal order in gradients, without introducing dissipative effects. In particular we note the appearance of a sound mode for s s -wave fracton superfluids. We show that previous work on fracton hydrodynamics falls into these classes. Finally, we study ultra-dense p p -wave fracton superfluids with a large kinetic mass in addition to studying the thermodynamics of ideal Aristotelian superfluids.
Momentum conservation is common in fluids, yet it may be incompatible with the hydrodynamics of theories with exotic conservation laws (such as fracton hydrodynamics) unless symmetries are spontaneously broken. Using the Martin-Siggia-Rose (MSR) effective field theory formalism, we develop a representation-theoretic framework for the hydrodynamics of translationally invariant systems with exotic conservation laws without spontaneous symmetry breaking. Under mild assumptions on the form of hydrodynamics, we show that such theories must satisfy two representation theoretic consistency conditions and a generalized Gauss's law constraint. Higher-form symmetries satisfy these conditions and we derive their ideal hydrodynamics; in three dimensions, the one-form case produces ideal non-relativistic magnetohydrodynamics. Finally, we prove that no other theories are compatible with momentum conservation in SO(3) nor SO(
d), for sufficiently large odd
d.
We extend recent work on hydrodynamics with global multipolar symmetries — known as “fracton hydrodynamics” — to systems in which the multipolar symmetries are gauged. We refer to the latter as “fracton magnetohydrodynamics”, in analogy to conventional magnetohydrodynamics (MHD), which governs systems with gauged charge conservation. We show that fracton MHD arises naturally from higher-rank Maxwell’s equations and in systems with one-form symmetries obeying certain constraints; while we focus on “minimal” higher-rank generalizations of MHD that realize diffusion, our methods may also be used to identify other, more exotic hydrodynamic theories (e.g., with magnetic subdiffusion). In contrast to semi-microscopic derivations of MHD, our approach elucidates the origin of the hydrodynamic modes by identifying the corresponding higher-form symmetries. Being rooted in symmetries, the hydrodynamic modes may persist even when the semi-microscopic equations no longer provide an accurate description of the system.
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.
Fracton theories possess exponentially degenerate ground states, excitations with restricted mobility, and nontopological higher-form symmetries. This paper shows that such theories can be defined on arbitrary spatial lattices in three dimensions. The key element of this construction is a generalization of higher-form gauge theories to so-called
Fp gauge theories, in which gauge transformations of rank-
k fields are specified by rank-
(k−p) gauge parameters. The
Z2 rank-two theory of type
F2, placed on a cubic lattice and coupled to scalar matter, is shown to have a topological phase exactly dual to the well-known X-cube model. Generalizations of this example yield novel fracton theories. In the continuum, the
U(1) rank-two theory of type
F2 is shown to have a perturbatively gapless fracton regime that cannot be consistently interpreted as a tensor gauge theory of any kind. The compact scalar fields that naturally couple to this
F2 theory also show gapless fracton behavior; on a cubic lattice they have a conserved
U(1) charge and dipole moment, but these particular charges are not necessarily conserved on more general lattices. The construction straightforwardly generalizes to
F2 theories of nonabelian rank-two gauge fields, giving first examples of pure nonabelian higher-rank theories.