Lattice Methods and Effective Field Theory

Abstract

Lattice field theory is a non-perturbative tool for studying properties of strongly interacting field theories, which is particularly amenable to numerical calculations and has quantifiable systematic errors. In these lectures we apply these techniques to nuclear Effective Field Theory (EFT), a nonrelativistic theory for nuclei involving the nucleons as the basic degrees of freedom. The lattice formulation of [1,2] for so-called pionless EFT is discussed in detail, with portions of code included to aid the reader in code development. Systematic and statistical uncertainties of these methods are discussed at length, and extensions beyond pionless EFT are introduced in the final Section.

A Guided Tour of ab initio Nuclear Many-Body Theory

“…Lattice methods are nowadays widely used to simulate the dynamics of non-perturbative field theories on finite spacetime lattices. The most prominent example is Lattice QCD, but implementations of various Effective Field Theories on the Lattice have been developed and applied with impressive outcomes in the past two decades-see, for example, references [172][173][174][175] and references therein, which also provide pedagogical introductions to Lattice EFT for nuclear systems.…”

“…Since the recognition of cutoff scales is an inherent aspect of EFTs, one can systematically correct for these effects [181,182]. The discrete lattice also breaks continuous spatial symmetries that may need to be restored approximately or exactly before comparisons with experimental data are made [172,182].…”

A Guided Tour of Ab Initio Nuclear Many-Body Theory

“…The most prominent example is Lattice QCD, but implementations of various Effective Field Theories on the Lattice have been developed and applied with impressive Hergert A Guided Tour of Ab Initio Nuclear Many-Body Theory outcomes in the past two decades -see, for example, Refs. [172,173,174,175,173] and references therein, which also provide pedagogical introductions to Lattice EFT for nuclear systems.…”

Worldline Approach to Few-Body Physics on the Lattice

“…Lattice formulations offer a window into the non-perturbative features of such theories. The state of the art methods are typically based on auxiliary field Monte Carlo techniques (see recent reviews [11,12] for lattice nuclear EFTs), which unfortunately suffer from sign problems in many cases of interest. This is even true for systems in one spatial dimension, which have recently become exciting due to the advent of experimental realizations with ultracold atoms in confining traps [13].…”