Topological Exchange Statistics in One Dimension
arXiv:2108.05653 · doi:10.1103/PhysRevA.105.052214
Abstract
The standard topological approach to indistinguishable particles formulates exchange statistics by using the fundamental group to analyze the connectedness of the configuration space. Although successful in two and more dimensions, this approach gives only trivial or near trivial exchange statistics in one dimension because two-body coincidences are excluded from configuration space. Instead, we include these path-ambiguous singular points and consider configuration space as an orbifold. This orbifold topological approach allows unified analysis of exchange statistics in any dimension and predicts novel possibilities for anyons in one-dimensional systems, including non-abelian anyons obeying alternate strand groups. These results clarify the non-topological origin of fractional statistics in one-dimensional anyon models.
v5: minor correction from v4; 16 pgs., 5 figs., 111 refs
References in corpus (19)
- Non-Abelian Anyons and Topological Quantum Computation
- Fractional statistics in anyon collisions
- The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics
- Anyon-fermion mapping and applications to ultracold gases in tight waveguides
- Fermionization and bosonization of expanding 1D anyonic fluids
- Correlation Functions of One-Dimensional Lieb-Liniger Anyons
- Pfaffian-like ground state for 3-body-hard-core bosons in 1D lattices
- Bosonic continuum theory of one-dimensional lattice anyons
- Bose-Fermi dualities for arbitrary one-dimensional quantum systems in the universal low energy regime
- Strongly interacting trapped one-dimensional quantum gases: an exact solution
- Quantum statistics on graphs
- Universal duality transformations in interacting one-dimensional quantum systems
- Three-body repulsive forces among identical bosons in one dimension
- Correlation functions of one-dimensional strongly interacting two-component gases
- A Generalization of the One-Dimensional Boson-Fermion Duality Through the Path-Integral Formalism
- Dynamically decoupled three-body interactions with applications to interaction-based quantum metrology
- Discrete Scale-Invariant Boson-Fermion Duality in One Dimension
- An explicit realization of fractional statistics in one dimension
- An Alexander type invariant for doodles
Cited by in corpus (11)
- Non-relativistic trace anomaly and equation of state in dense fermionic matter
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- Beyond braid statistics: Constructing a lattice model for anyons with exchange statistics intrinsic to one dimension
- Quantum Walk on Orbit Spaces
- Virtual planar braid groups and permutations
- Chirally-protected state manipulation by tuning one-dimensional statistics
- Topologically Nontrivial Three-Body Contact Interaction in One Dimension
- Congruence subgroups and crystallographic quotients of small Coxeter groups
- Universal properties and dynamical bosonization of strongly interacting one-dimensional anyons
- Introduction to abelian anyons in planar systems