Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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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