Preprint Article Version 1 This version is not peer-reviewed

Exponents of spectral functions in the one-dimensional Bose gas

Version 1 : Received: 20 September 2018 / Approved: 20 September 2018 / Online: 20 September 2018 (16:21:50 CEST)

A peer-reviewed article of this Preprint also exists.

Schlottmann, P. Exponents of Spectral Functions in the One-Dimensional Bose Gas. Condens. Matter 2018, 3, 35. Schlottmann, P. Exponents of Spectral Functions in the One-Dimensional Bose Gas. Condens. Matter 2018, 3, 35.

Journal reference: Condens. Matter 2018, 3, 35
DOI: 10.3390/condmat3040035

Abstract

The one-dimensional gas of bosons interacting via a repulsive contact potential was solved long ago via Bethe's ansatz by Lieb and Liniger [Phys. Rev. {\bf 130}, 1605 (1963)]. The low energy excitation spectrum is a Luttinger liquid parametrized by a conformal field theory with conformal charge $c=1$. For higher energy excitations the spectral function displays deviations from the Luttinger behavior arising from the curvature terms in the dispersion. Adding a corrective term of the form of a mobile impurity coupled to the Luttinger liquid modes corrects this problem. The ``impurity'' term is an irrelevant operator, which if treated non-perturbatively, yields the threshold singularities in the one-particle and one-hole hole Green's function correctly. We show that the exponents obtained via the finite size corrections to the ground state energy are identical to those obtained through the shift function.

Subject Areas

Bose gas, Bethe ansatz, threshold singularity

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