From hardcore Bosons to free Fermions with Painlev{é} V

Abstract

We calculate zero temperature Green's function, the density--density correlation and expectation values of a one--dimensional quantum particle which interacts with a Fermi--sea via a $\delta$--potential. The eigenfunctions of the Bethe-Ansatz solvable model can be expressed as a determinant. This allows us to obtain a compact expression for the Green's function of the extra particle. In the hardcore limit the resulting expression can be analysed further using Painlev{é} V transcendents. It is found that depending on the extra particles momentum its Green's function undergoes a transition of that for hardcore Bosons to that of free Fermions.

27 pages, 7 figures, published version

References in corpus (4)

• One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
• Bosonizing one-dimensional cold atomic gases
• Renormalization Group Theory for the Imbalanced Fermi Gas
• Analytic solutions of the 1D finite coupling delta function Bose gas

Cited by in corpus (8)

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• Contact and Structure Factor for Bosonic and Fermionic Mixtures
• Necessary and sufficient condition for quantum adiabaticity in a driven one-dimensional impurity-fluid system
• Mobile impurity in a one-dimensional gas at finite temperatures
• Kubo-Martin-Schwinger relation for an interacting mobile impurity
• Quantum Many-Body Adiabaticity, Topological Thouless Pump and Driven Impurity in a One-Dimensional Quantum Fluid
• One-dimensional Fermi polaron after a kick: two-sided singularity of the momentum distribution, Bragg reflection and other exact results