CMSA Quantum Matter/Quantum Field Theory Seminar: Jordan-Wigner dualities for translation-invariant Hamiltonians in any dimension

Inspired by recent constructions of Jordan-Wigner transformations in higher dimensions by Kapustin et. al., I will present a framework for an exact bosonization, which locally maps a translation-invariant model of spinless fermions to a gauge theory of Pauli spins. I will show that the duality exists for an arbitrary number of (possibly many-body) "hopping" operators in any dimension and provide an explicit construction. The duality can be concisely stated in terms of an algebraic formalism of translation-invariant Hamiltonians proposed by Haah.

I will then present two interesting applications. First, bosonizing Majorana stabilizer codes, such as the Majorana color code or the checkerboard model, into Pauli stabilizer codes. Second, bosonizing fermionic systems where fermion parity is conserved on submanifolds such as higher-form, line, planar or fractal symmetry. In 3+1D, the latter two can give rise to fracton models where emergent particles are immobile, but yet can be ``fermionic". This may give rise to new non-relativistic 't Hooft anomalies.