A Generalization of the One-Dimensional Boson-Fermion Duality Through the Path-Integral Formalism

Abstract

We study boson-fermion dualities in one-dimensional many-body problems of identical particles interacting only through two-body contacts. By using the path-integral formalism as well as the configuration-space approach to indistinguishable particles, we find a generalization of the boson-fermion duality between the Lieb-Liniger model and the Cheon-Shigehara model. We present an explicit construction of $n$-boson and $n$-fermion models which are dual to each other and characterized by $n-1$ distinct (coordinate-dependent) coupling constants. These models enjoy the spectral equivalence, the boson-fermion mapping, and the strong-weak duality. We also discuss a scale-invariant generalization of the boson-fermion duality.

19 pages, 9 eepic figures; typos corrected, references added, discussion section expanded

References in corpus (5)

• Anyon-fermion mapping and applications to ultracold gases in tight waveguides
• A variational approach to repulsively interacting three-fermion systems in a one-dimensional harmonic trap
• Quantum statistics on graphs
• Theoretical construction of 1D anyon models
• Quantization and superselection sectors III: Multiply connected spaces and indistinguishable particles

Cited by in corpus (6)

• Topological Exchange Statistics in One Dimension
• Discrete Scale-Invariant Boson-Fermion Duality in One Dimension
• Duality between weak and strong interactions in quantum gases
• Beyond braid statistics: Constructing a lattice model for anyons with exchange statistics intrinsic to one dimension
• Quantum Walk on Orbit Spaces
• Topologically Nontrivial Three-Body Contact Interaction in One Dimension