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 MonteCarlo 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.
Highlights
We study the quantum field theory of a charged φ4 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
Introduction.—It is well known that phenomena in low energy physics can be described in terms of a few low energy parameters, which in the context of this Letter was, e.g., discussed in the seminal paper [1]
As a particular instance of this relation the condensation of particles at low temperature and nonzero chemical potential can be related to scattering data of the corresponding quantum field theory
Summary
We study the quantum field theory of a charged φ4 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. As a particular instance of this relation the condensation of particles at low temperature and nonzero chemical potential can be related to scattering data of the corresponding quantum field theory. One may show [2] that the critical values of the chemical potential where one observes condensation steps at low temperature and small volume are related to the finite volume many particle energies, which in turn are related to the scattering length [1].
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