Anyons from Three-Body Hard-Core Interactions in One Dimension
arXiv:1803.11000 · doi:10.1016/j.aop.2019.168003
Abstract
Traditional anyons in two dimensions have generalized exchange statistics governed by the braid group. By analyzing the topology of configuration space, we discover that an alternate generalization of the symmetric group governs particle exchanges when there are hard-core three-body interactions in one-dimension. We call this new exchange symmetry the traid group and demonstrate that it has abelian and non-abelian representations that are neither bosonic nor fermionic, and which also transform differently under particle exchanges than braid group anyons. We show that generalized exchange statistics occur because, like hard-core two-body interactions in two dimensions, hard-core three-body interactions in one dimension create defects with co-dimension two that make configuration space no longer simply-connected. Ultracold atoms in effectively one-dimensional optical traps provide a possible implementation for this alternate manifestation of anyonic physics.
arXiv comment34 pages double spaced, 8 figures, 85 refs. In v4, Sects. 1, 2, and references are revised
References in corpus (35)
- Fault-tolerant quantum computation by anyons
- Non-Abelian Anyons and Topological Quantum Computation
- Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
- Atomic three-body loss as a dynamical three-body interaction
- Statistically induced Phase Transitions and Anyons in 1D Optical Lattices
- Exact Dynamical Correlation Functions of Calogero-Sutherland Model and One-Dimensional Fractional Statistics
- Exact solution of double-delta function Bose gas through interacting anyon gas
- Fractional Statistics in One-Dimension: View From An Exactly Solvable Model
- The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics
- Anyon-fermion mapping and applications to ultracold gases in tight waveguides
- Floquet realization and signatures of one-dimensional anyons in an optical lattice
- Nonequilibrium dynamics of one-dimensional hard-core anyons following a quench: Complete relaxation of one-body observables
- Correlation Functions of One-Dimensional Lieb-Liniger Anyons
- Symmetries of Three Harmonically-Trapped Particles in One Dimension
- Ground-state properties of hard-core anyons in one-dimensional optical lattices
- One-dimensional three-boson problem with two- and three-body interactions
- Pfaffian-like ground state for 3-body-hard-core bosons in 1D lattices
- Exact diagonalization of the one dimensional Bose-Hubbard model with local 3-body interactions
- Exact Groundstates of Rotating Bose Gases close to a Feshbach Resonance
- Universal bound states of one-dimensional bosons with two- and three-body attractions
- Quantum anomaly and thermodynamics of one-dimensional fermions with three-body interactions
- Strongly interacting mesoscopic systems of anyons in one dimension
- First order phase transitions in optical lattices with tunable three-body onsite interaction
- A Hubbard model for ultracold bosonic atoms interacting via zero-point-energy induced three-body interactions
- Ideal quantum gases in two dimensions
- Strongly repulsive anyons in one dimension
- Nonabelian braid statistics versus projective permutation statistics
- Three-body interaction effects on the ground state of one-dimensional anyons
- Ground-state properties of dilute one-dimensional Bose gas with three-body repulsion
- Dynamically decoupled three-body interactions with applications to interaction-based quantum metrology
- The three-body pseudo-potential for atoms confined in one dimension
- Mott lobes of the Bose-Hubbard model with three-body interactions
- An explicit realization of fractional statistics in one dimension
- The Goldilocks model of separable, zero-range, few-body interactions in one-dimensional harmonic traps
- Coincidence Structures and Hard-Core Few-Body Interactions
Cited by in corpus (18)
- Topological Exchange Statistics in One Dimension
- Cooper Triples in Attractive Three-Component Fermions: Implication for Hadron-Quark Crossover
- Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature
- Structure and automorphisms of pure virtual twin groups
- Conjugacy classes and automorphisms of twin groups
- Non-relativistic trace anomaly and equation of state in dense fermionic matter
- Exploring Many-body Interactions Through Quantum Fisher Information
- Three-body bound states of two bosons and one impurity in one dimension
- Beyond braid statistics: Constructing a lattice model for anyons with exchange statistics intrinsic to one dimension
- Virtual planar braid groups and permutations
- Congruence subgroups and crystallographic quotients of small Coxeter groups
- Topologically Nontrivial Three-Body Contact Interaction in One Dimension
- Nonequilibrium dynamics in one-dimensional strongly interacting two-component gases
- Fermionic anyons: entanglement and quantum computation from a resource-theoretic perspective
- Lattice-enabled detection of spin-dependent three-body interactions
- Universal properties and dynamical bosonization of strongly interacting one-dimensional anyons
- Scale Invariance Breaking and Discrete Phase Invariance in Few-Body Problems
- Flat braid groups, right-angled Artin groups, and commensurability