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Abstract Emergence of fundamental forces from gauge symmetry is among our most profound insights about the physical universe. In nature, such symmetries remain hidden in the space of internal degrees of freedom of subatomic particles. Here we propose a way to realize and study gauge structures in real space, manifest in external degrees of freedom of quantum states. We present a model based on a ring-shaped lattice potential, which allows for both Abelian and non-Abelian constructs. Non trivial Wilson loops are shown possible via physical motion of the system. The underlying physics is based on the close analogy of geometric phase with gauge potentials that has been utilized to create synthetic gauge fields with internal states of ultracold atoms. By scaling up to an array with spatially varying parameters, a discrete gauge field can be realized in position space, and its dynamics mapped over macroscopic size and time scales.
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Dynamical Abelian anyons with bound states and scattering states
We introduce a family of quantum spin Hamiltonians on Z2 that can be regarded as perturbations of Kitaev’s Abelian quantum double models that preserve the gauge and duality symmetries of these models. We analyze in detail the sector with one electric charge and one magnetic flux and show that the spectrum in this sector consists of both bound states and scattering states of Abelian anyons. Concretely, we have defined a family of lattice models in which Abelian anyons arise naturally as finite-size quasi-particles with non-trivial dynamics that consist of a charge-flux pair. In particular, the anyons exhibit a non-trivial holonomy with a quantized phase, consistent with the gauge and duality symmetries of the Hamiltonian.
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- Award ID(s):
- 2108390
- PAR ID:
- 10523623
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- Journal of Mathematical Physics
- Volume:
- 64
- Issue:
- 7
- ISSN:
- 0022-2488
- Page Range / eLocation ID:
- 071903
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0151232
