Lattice Effective Field Theory Simulations of Nuclei

TL;DR

This review surveys lattice nuclear effective field theory (NLEFT) as an ab initio framework for low-energy nuclear physics, outlining how chiral EFT interactions organized by powers of $Q$ are implemented on a spacetime lattice with spacing $\sim$1 fm. It catalogs a suite of methodologies—Euclidean-time projection, auxiliary-field Monte Carlo, spherical-wall scattering, wavefunction matching, pinhole/pinhole-trace techniques, adiabatic projection, floating block, and rank-one operator insertions—that enable precise calculations of light-to-medium nuclei, nuclear-matter thermodynamics, and cluster phenomena, while addressing sign problems through symmetry and perturbative strategies. The review highlights concrete achievements, including accurate binding energies, radii, density distributions, and phase shifts up to $\text{N3LO}$, as well as insights into nuclear matter and collision initial states. The work emphasizes the complementary role of lattice EFT alongside other ab initio methods and points to ongoing developments toward hypernuclei and hyperneutron matter with potential impact on astrophysical and collider phenomenology.

Abstract

Lattice effective field theory applies the principles of effective field theory in a lattice framework where space and time are discretized. Nucleons are placed on the lattice sites, and the interactions are tuned to replicate the observed features of the nuclear force. Monte Carlo simulations are then employed to predict the properties of nuclear few- and many-body systems. We review the basic methods and several theoretical and algorithmic advances that have been used to further our understanding of atomic nuclei.

Figures (6)

• Figure 1: Neutron-proton scattering phase shifts and mixing angles with theoretical uncertainties versus the relative momenta for $a = 1.32~{\rm fm}$. Blue, green, and red bands signify the estimated uncertainties at NLO, N2LO, and N3LO, respectively. The black solid line and diamonds denote the phase shift or mixing angle from the Nijmegen partial-wave analysis Stoks:1993tb and lattice calculation at N3LO, respectively. Figure taken with permission from Ref. Li:2018ymw.
• Figure 2: Panel a shows the Euclidean-time evolution using projection Monte Carlo. Panel b shows the interactions of individual nucleons with auxiliary fields and pion fields.
• Figure 3: A unitary transformation is used produce a new Hamiltonian $H'$ that is close to $H^S$. In each two-body channel, the ground state wavefunction of $H'$ matches the ground state wavefunction of $H$ for $r > R$ and is proportional to the ground state wavefunction of $H^S$ for $r < R$, with constant of proportionality close to $1$. Figure taken with permission from Ref. Elhatisari:2022zrb.
• Figure 4: Panel a shows the pinhole algorithm with pinholes inserted in the midpoint of the Euclidean time evolution. Panel b shows the pinhole trace algorithm with the same pinholes inserted at the beginning and end of the Euclidean time evolution for the partition function, ${\rm Tr} \exp(-\beta H)$.
• Figure 5: Intrinsic nucleon densities for several low-lying states of $^{12}$C. Panels a through f show the angles of the triangle formed by the three alpha clusters. Panels g through l show the intrinsic densities. Figure taken with permission from Ref. Shen:2022bak.