# Finite Density Condensation and Scattering Data: A Study in ${\varphi }^{4}$ Lattice Field Theory

Gattringer, Christof (Universität Graz, Institut für Physik, Universitätsplatz 5, 8010 Graz, Austria) ; Giuliani, Mario (Universität Graz, Institut für Physik, Universitätsplatz 5, 8010 Graz, Austria) ; Orasch, Oliver (Universität Graz, Institut für Physik, Universitätsplatz 5, 8010 Graz, Austria)

11 June 2018

Abstract: We study the quantum field theory of a charged ${\varphi }^{4}$ 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 $\mu$ is overcome by using a worldline representation for the Monte Carlo simulation. At low temperature we study the particle number as a function of $\mu$ and observe the steps for 1-, 2-, and 3-particle condensation. We determine the corresponding critical values ${\mu }_{n}^{\mathrm{crit}}$, $n=1$, 2, 3 and analyze their dependence on the spatial extent $L$ of the lattice. Linear combinations of the ${\mu }_{n}^{\mathrm{crit}}$ 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.

Published in: Physical Review Letters 120 (2018)