Journal of High Energy Physics

, 2019:248 | Cite as

Continuum limit Tonks-Girardeau matrix elements. Part I. The ground state and the uniform density state

  • Jarah EvslinEmail author
  • Hosam Mohammed
  • Hui Liu
  • Yao Zhou
Open Access
Regular Article - Theoretical Physics


The Tonks-Girardeau model is a quantum mechanical model of N impenetrable bosons in 1+1 dimensions. A Vandermonde determinant provides the exact N -particle wave function of the ground state, or equivalently the matrix elements with respect to position eigenstates. We consider the large N limit of these matrix elements. We present a binning prescription which calculates the leading terms of the matrix elements in a time which is independent of N, and so is suitable for this limit. In this sense, it allows one to solve for the ground state of a strongly coupled continuum quantum field theory in the field eigenstate basis. As examples, we calculate the matrix elements with respect to states with uniform density and also states consisting of two regions with distinct densities.


Bethe Ansatz Integrable Field Theories Field Theories in Lower Dimensions Lattice Integrable Models 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited


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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Jarah Evslin
    • 1
    • 2
    Email author
  • Hosam Mohammed
    • 1
    • 2
  • Hui Liu
    • 1
    • 2
  • Yao Zhou
    • 1
    • 2
  1. 1.Institute of Modern PhysicsLanzhouChina
  2. 2.China University of the Chinese Academy of SciencesBeijingChina

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