Grand canonical ensemble, multi-particle wave functions, scattering data, and lattice field theories

TL;DR

This paper demonstrates how scattering data in quantum field theories can be extracted from finite density lattice simulations, using dual formulations and Monte Carlo methods, providing new tools for non-perturbative analysis.

Contribution

It introduces a dual lattice formulation that enables extraction of scattering data from finite density simulations, applicable to models like the 2D O(3) model.

Findings

Scattering phase shifts can be obtained from chemical potential thresholds.

Wave functions in the 2-particle sector yield accurate phase shifts.

Dual Monte Carlo simulations successfully reproduce exact results.

Abstract

We show that information about scattering data of a quantum field theory can be obtained from studying the system at finite density and low temperatures. In particular we consider models formulated on the lattice which can be exactly dualized to theories of conserved charge fluxes on lattice links. Apart from eliminating the complex action problem at nonzero chemical potential mu, these dualizations allow for a particle world line interpretation of the dual fluxes from which one can extract data about the 2-particle wave function. As an example we perform dual Monte Carlo simulations of the 2-dimensional O(3) model at nonzero mu and finite volume, whose non-perturbative spectrum consists of a massive triplet of particles. At nonzero mu particles are induced in the system, which at sufficiently low temperature give rise to sectors of fixed particle number. We show that the scattering phase shifts can be obtained either from the critical chemical potential values separating the sectors or directly from the wave function in the 2-particle sector. We find that both methods give excellent agreement with the exact result. We discuss the applicability and generality of the new approaches.