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Condens. Matter 2018, 3(4), 35; https://doi.org/10.3390/condmat3040035

Exponents of Spectral Functions in the One-Dimensional Bose Gas

Department of Physics, Florida State University, Tallahassee, FL 32306, USA
Received: 20 September 2018 / Revised: 13 October 2018 / Accepted: 16 October 2018 / Published: 23 October 2018
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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 (Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State). 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 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. View Full-Text
Keywords: Bose gas; Bethe ansatz; threshold singularities Bose gas; Bethe ansatz; threshold singularities
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Schlottmann, P. Exponents of Spectral Functions in the One-Dimensional Bose Gas. Condens. Matter 2018, 3, 35.

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