Journal
PHYSICAL REVIEW A
Volume 103, Issue 2, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.103.L021302
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Funding
- NSFC [12050410239]
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The study developed a general theory of local unitary transformations between one-dimensional quantum systems of bosons and fermions with various low-energy interactions. These transformations generate families of duality relations and models linking the strong- and weak-coupling limits of the respective dual theories.
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 nonrelativistic, relativistic, or otherwise-and low-energy interactions in the universal regime. These transformations generate families of duality relations and models that relate the strong- and weak-coupling limits of the respective dual theories.
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