Effective field theory of interactions on the lattice

TL;DR

This paper presents a simple lattice-based method for systematically renormalizing effective field theory interactions, facilitating the study of multi-parameter interactions in discretized quantum systems.

Contribution

It introduces a straightforward approach to renormalize effective field theory interactions on a lattice, applicable to both one-dimensional and three-dimensional s-wave collision problems.

Findings

Established a relation between lattice and continuum coupling constants.

Demonstrated the method's effectiveness in simple quantum collision models.

Provided a systematic framework for renormalization with multiple interaction parameters.

Abstract

We consider renormalization of effective field theory interactions by discretizing the continuum on a tight-binding lattice. After studying the one-dimensional problem, we address s-wave collisions in three dimensions and relate the bare lattice coupling constants to the continuum coupling constants. Our method constitutes a very simple avenue for the systematic renormalization in effective field theory, and is especially useful as the number of interaction parameters increases.