Constraints of kinematic bosonization in two and higher dimensions

Abstract

Contrary to the common wisdom, local bosonizations of fermionic systems exist in higher dimensions. Interestingly, resulting bosonic variables must satisfy local constraints of a gauge type. They effectively replace long distance exchange interactions. In this work we study in detail the properties of such a system which was proposed a long time ago. In particular, dependence of the constraints on lattice geometry and fermion multiplicity is further elaborated and is now classified for all two dimensional, rectangular lattices with arbitrary sizes. For few small systems the constraints are solved analytically and the complete spectra of reduced spin hamiltonias are shown to agree with the original fermionic ones. The equivalence is extended to fermions in an external Wegner $Z_2$ field. It is also illustrated by an explicit calculation for a particular configuration of Wegner variables. Finally, a possible connection with the recently proposed web of dualities is discussed.

arXiv commentdiscussion of dualities and the outlook added, references updated, 18 pages, 1 figure, 5 tables

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Cited by in corpus (8)

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• Higher-dimensional Jordan-Wigner Transformation and Auxiliary Majorana Fermions
• Variational solutions to fermion-to-qubit mappings in two spatial dimensions
• Bosonization based on Clifford algebras and its gauge theoretic interpretation
• Low-depth simulations of fermionic systems on square-grid quantum hardware
• Error-correcting codes for fermionic quantum simulation
• Bosonization of Majorana modes and edge states
• On the locality of qubit encodings of local fermionic modes