Finite Density Condensation and Scattering Data: A Study in ϕ^{4} Lattice Field Theory.


Journal Article

We study the quantum field theory of a charged ϕ^{4} field in lattice regularization at finite density and low temperature in 2 and 4 dimensions with the goal of analyzing the connection of condensation phenomena to scattering data in a nonperturbative way. The sign problem of the theory at nonzero chemical potential μ is overcome by using a worldline representation for the Monte Carlo simulation. At low temperature we study the particle number as a function of μ and observe the steps for 1-, 2-, and 3-particle condensation. We determine the corresponding critical values μ_{n}^{crit}, n=1, 2, 3 and analyze their dependence on the spatial extent L of the lattice. Linear combinations of the μ_{n}^{crit} give the interaction energies in the 2- and 3-particle sectors and their dependence on L is related to scattering data by Lüscher's formula and its generalizations to three particles. For two dimensions we determine the scattering phase shift and for four dimensions the scattering length. We cross-check our results with a determination of the mass and the 2- and 3-particle energies from conventional 2-, 4-, and 6-point correlators at zero chemical potential. The letter demonstrates that the physics of condensation at finite density and low temperature is closely related to scattering data of a quantum field theory.

Full Text

Cited Authors

  • Gattringer, C; Giuliani, M; Orasch, O

Published Date

  • June 2018

Published In

Volume / Issue

  • 120 / 24

Start / End Page

  • 241601 -

PubMed ID

  • 29956962

Pubmed Central ID

  • 29956962

Electronic International Standard Serial Number (EISSN)

  • 1079-7114

International Standard Serial Number (ISSN)

  • 0031-9007

Digital Object Identifier (DOI)

  • 10.1103/physrevlett.120.241601


  • eng