Machian fractons, Hamiltonian attractors and non-equilibrium steady states
arXiv:2312.02271 · doi:10.1103/PhysRevB.110.024305
Abstract
We study the fracton problem in classical mechanics, with fractons defined as point particles that conserve multipole moments up to a given order. We find that the nonlinear Machian dynamics of the fractons is characterized by late-time attractors in position-velocity space for all , despite the absence of attractors in phase space dictated by Liouville's theorem. These attractors violate ergodicity and lead to non-equilibrium steady states, which always break translational symmetry, even in spatial dimensions where the Hohenberg-Mermin-Wagner-Coleman theorem for equilibrium systems forbids such breaking. While a full understanding of the many-body nonlinear problem is a formidable and incomplete task, we provide a conceptual understanding of our results using an adiabatic approximation for the late-time trajectories and an analogy with the idea of `order-by-disorder' borrowed from equilibrium statistical mechanics. Altogether, these fracton systems host a new paradigm for Hamiltonian dynamics and non-equilibrium many-body physics.
arXiv comment12 pages, 11 figures, v2: minor changes, close to published version
References in corpus (24)
- Many body localization and thermalization in quantum statistical mechanics
- Noncommutative Perturbative Dynamics
- Local stabilizer codes in three dimensions without string logical operators
- Spin-lattice coupling in frustrated antiferromagnets
- Quantum Glassiness
- Fractons
- Localization from Hilbert space shattering: from theory to physical realizations
- Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet
- Local constraints can globally shatter Hilbert space: a new route to quantum information protection
- Localization protected quantum order
- 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
- Fracton Phases of Matter
- Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains
- Towards classification of Fracton phases: the multipole algebra
- Localization in fractonic random circuits
- Kinetically constrained freezing transition in a dipole-conserving system
- Stark many-body localization on a superconducting quantum processor
- Symmetry constraints on many-body localization
- Hohenberg-Mermin-Wagner-type theorems and dipole symmetry
- Exact solution for the filling-induced thermalization transition in a 1D fracton system
- Eigenstate phases with finite on-site non-Abelian symmetry
- Fractonic plaquette-dimer liquid beyond renormalization
- Classical Non-Relativistic Fractons