Finite Density Condensation and Scattering Data: A Study in ϕ^{4} Lattice Field Theory
Abstract
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 3particle 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 3particle 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 crosscheck our results with a determination of the mass and the 2 and 3particle energies from conventional 2, 4, and 6point 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.
 Publication:

Physical Review Letters
 Pub Date:
 June 2018
 DOI:
 10.1103/PhysRevLett.120.241601
 arXiv:
 arXiv:1804.01580
 Bibcode:
 2018PhRvL.120x1601G
 Keywords:

 High Energy Physics  Lattice;
 High Energy Physics  Phenomenology
 EPrint:
 Comments and two references added. Final version to appear in Physical Review Letters