Classical Non-Relativistic Fractons

Abstract

We initiate the study of the classical mechanics of non-relativistic fractons in its simplest setting - that of identical one dimensional particles with local Hamiltonians characterized by by a conserved dipole moment in addition to the usual symmetries of space and time translation invariance. We introduce a family of models and study the $N$ body problem for them. We find that locality leads to a ``Machian" dynamics in which a given particle exhibits finite inertia only if within a specified distance of at least another one. For well separated particles this leads to immobility, much as for quantum models of fractons discussed before. For two or more particles within inertial reach of each other at the start of motion we get an interesting interplay of inertia and interactions. Specifically for a solvable ``inertia only" model of fractons we find that $N=2$ particles always become immobile at long times. Remarkably $N=3$ particles generically evolve to a late time state with one immobile particle and two that oscillate about a common center of mass with generalizations of such ``Machian clusters" for $N>3$ . Interestingly, Machian clusters exhibit physical limit cycles in a Hamiltonian system even though mathematical limit cycles are forbidden by Liouville's theorem.

arXiv comment22 pages, 28 figures, v2: improved presentation, expanded discussion, close to published version

References in corpus (30)

• Noncommutative Perturbative Dynamics
• Local stabilizer codes in three dimensions without string logical operators
• Braiding statistics approach to symmetry-protected topological phases
• Eigenstate Thermalization Hypothesis
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Quantum Glassiness
• Fractons
• Localization from Hilbert space shattering: from theory to physical realizations
• Local constraints can globally shatter Hilbert space: a new route to quantum information protection
• Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
• Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians
• A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations
• Topological quantum order: stability under local perturbations
• Fracton Phases of Matter
• Absolute Stability and Spatiotemporal Long-Range Order in Floquet systems
• Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains
• Fracton hydrodynamics
• The Fracton Gauge Principle
• Towards classification of Fracton phases: the multipole algebra
• Emergent Gravity of Fractons: Mach's Principle Revisited
• Kinetically constrained freezing transition in a dipole-conserving system
• Emergent Phases of Fractonic Matter
• Stark many-body localization on a superconducting quantum processor
• The Lense--Thirring Effect and Mach's Principle
• Fractonic Luttinger Liquids and Supersolids in a Constrained Bose-Hubbard Model
• Dipole condensates in tilted Bose-Hubbard chains
• Hohenberg-Mermin-Wagner-type theorems and dipole symmetry
• Exact solution for the filling-induced thermalization transition in a 1D fracton system
• Classical Mechanics without Absolute Space
• Fractonic plaquette-dimer liquid beyond renormalization

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• Classical Fractons: Local chaos, global broken ergodicity and an arrow of time
• Fracton and Non-Lorentzian Particle Duality: Gauge Field Couplings and Geometric Implications
• The spin-orbital Kitaev model: from kagome spin ice to classical fractons
• Machian fractons, Hamiltonian attractors and non-equilibrium steady states
• Universal Freezing Transitions of Dipole-Conserving Chains
• Phase space fractons
• Continuum Fractons: Quantization and the Few Body Problem