Universal duality transformations in interacting one-dimensional quantum systems

Abstract

One-dimensional quantum systems admit duality relations that put hard core spinless bosons and fermions in one-to-one correspondence via Girardeau's mapping theorem. The simplest models of soft bosons interacting via zero-range potentials can also be mapped onto dual interacting fermions. However, a systematic approach to one-dimensional statistical transmutation for arbitrary low-energy interactions in the spinless and spinful or multicomponent cases has remained elusive. I develop a general theory of local unitary transformations between one-dimensional quantum systems of bosons and fermions with arbitrary spin or internal structure, single-particle dispersion -- including non-relativistic, relativistic or otherwise -- and low-energy interactions in the universal regime. These transformations generate families of new duality relations and models that relate the strong and weak coupling limits of the respective dual theories.

arXiv comment5 pages, 1 figure. See accompanying article "Bose-Fermi dualities for arbitrary one-dimensional quantum systems in the universal low energy regime", arXiv:2009.00624

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• Topological Exchange Statistics in One Dimension
• Cooper Triples in Attractive Three-Component Fermions: Implication for Hadron-Quark Crossover
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• Condensation of Cooper Triples
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