Jordan-Wigner dualities for translation-invariant Hamiltonians in any dimension: Emergent fermions in fracton topological order
Nathanan Tantivasadakarn
Abstract
The author generalizes the Jordan-Wigner Transformation to any translation-invariant fermion system, including cases where fermion parity is conserved on individual subdimensional manifolds, such as planes or fractals. The paper finds that in three dimensions, the dual spin model is an exotic gauge theory where point-like excitations have fundamentally restricted mobility called fractons, yet simultaneously are emergent fermions.
Topics & Concepts
FermionPhysicsGauge theoryTheoretical physicsParity (physics)Order (exchange)Transformation (genetics)Spin (aerodynamics)Topology (electrical circuits)Gauge (firearms)Quantum mechanicsConserved quantityDual (grammatical number)FractonIdeal (ethics)Topological orderQuantum many-body systemsAlgebraic structures and combinatorial modelsQuasicrystal Structures and Properties