Low Energy Continuum and Lattice Effective Field Theories

In the first part of the thesis we consider the constraints of causality and unitarity for particles interacting via strictly finite-range interactions. We generalize Wigner's causality bound to the case of non-vanishing partial-wave mixing. Specifically we analyze the system of the low-energy interactions between protons and neutrons. We also analyze low-energy scattering for systems with arbitrary short-range interactions plus an attractive $1/r^{\alpha}$ tail for $\alpha\geq2$. In particular, we focus on the case of $\alpha=6$ and we derive the constraints of causality and unitarity also for these systems and find that the van der Waals length scale dominates over parameters characterizing the short-distance physics of the interaction. This separation of scales suggests a separate universality class for physics characterizing interactions with an attractive $1/r^{6}$ tail. We argue that a similar universality class exists for any attractive potential $1/r^{\alpha}$ for $\alpha\geq2$. In the second part of the thesis we present lattice Monte Carlo calculations of fermion-dimer scattering in the limit of zero-range interactions using the adiabatic projection method. The adiabatic projection method uses a set of initial cluster states and Euclidean time projection to give a systematically improvable description of the low-lying scattering cluster states in a finite volume. We use L\"uscher's finite-volume relations to determine the $s$-wave, $p$-wave, and $d$-wave phase shifts. For comparison, we also compute exact lattice results using Lanczos iteration and continuum results using the Skorniakov-Ter-Martirosian equation. For our Monte Carlo calculations we use a new lattice algorithm called impurity lattice Monte Carlo. This algorithm can be viewed as a hybrid technique which incorporates elements of both worldline and auxiliary-field Monte Carlo simulations.Comment: Ph.D. thesis, 201 pages, 19 figures, 17 table

Ab initio calculation of the alpha-particle monopole transition form factor: No puzzle for nuclear forces

We present a parameter-free ab initio calculation of the $\alpha$-particle monopole transition form factor in the framework of nuclear lattice effective field theory. We use a minimal nuclear interaction that was previously used to reproduce the ground state properties of light nuclei, medium-mass nuclei, and neutron matter simultaneously with no more than a few percent error in the energies and charge radii. The results for the monopole transition form factor are in good agreement with recent precision data from Mainz.Comment: 5 pages, 3 figure

Ab initio study of nuclear clustering in hot dilute nuclear matter

We present a systematic ab initio study of clustering in hot dilute nuclear matter using nuclear lattice effective field theory with an SU(4)-symmetric interaction. We introduce a method called light-cluster distillation to determine the abundances of dimers, trimers, and alpha clusters as a function of density and temperature. Our lattice results are compared with an ideal gas model composed of free nucleons and clusters. Excellent agreement is found at very low density, while deviations from ideal gas abundances appear at increasing density due to cluster-nucleon and cluster-cluster interactions. In addition to determining the composition of hot dilute nuclear matter as a function of density and temperature, the lattice calculations also serve as benchmarks for virial expansion calculations, statistical models, and transport models of fragmentation and clustering in nucleus-nucleus collisions.Comment: 6+8 pages, 4+8 figure

Lattice Monte Carlo Simulations with Two Impurity Worldlines

We develop the impurity lattice Monte Carlo formalism, for the case of two distinguishable impurities in a bath of polarized fermions. The majority particles are treated as explicit degrees of freedom, while the impurities are described by worldlines. The latter serve as localized auxiliary fields, which affect the majority particles. We apply the method to non-relativistic three-dimensional systems of two impurities and a number of majority particles where both the impurity-impurity interaction and the impurity-majority interaction have zero range. We consider the case of an attractive impurity-majority interaction, and we study the formation and disintegration of bound states as a function of the impurity-impurity interaction strength. We also discuss the potential applications of this formalism to other quantum many-body systems.Comment: 7 pages, 4 figure

Nuclear binding near a quantum phase transition

How do protons and neutrons bind to form nuclei? This is the central question of ab initio nuclear structure theory. While the answer may seem as simple as the fact that nuclear forces are attractive, the full story is more complex and interesting. In this work we present numerical evidence from ab initio lattice simulations showing that nature is near a quantum phase transition, a zero-temperature transition driven by quantum fluctuations. Using lattice effective field theory, we perform Monte Carlo simulations for systems with up to twenty nucleons. For even and equal numbers of protons and neutrons, we discover a first-order transition at zero temperature from a Bose-condensed gas of alpha particles (4He nuclei) to a nuclear liquid. Whether one has an alpha-particle gas or nuclear liquid is determined by the strength of the alpha-alpha interactions, and we show that the alpha-alpha interactions depend on the strength and locality of the nucleon-nucleon interactions. This insight should be useful in improving calculations of nuclear structure and important astrophysical reactions involving alpha capture on nuclei. Our findings also provide a tool to probe the structure of alpha cluster states such as the Hoyle state responsible for the production of carbon in red giant stars and point to a connection between nuclear states and the universal physics of bosons at large scattering length.Comment: Published version to appear in Physical Review Letters. Main: 5 pages, 3 figures. Supplemental material: 13 pages, 6 figure

Hidden spin-isospin exchange symmetry

The strong interactions among nucleons have an approximate spin-isospin exchange symmetry that arises from the properties of quantum chromodynamics in the limit of many colors, $N_c$. However this large-$N_c$ symmetry is well hidden and reveals itself only when averaging over intrinsic spin orientations. Furthermore, the symmetry is obscured unless the momentum resolution scale is close to an optimal scale that we call $\Lambda_{{\rm large-}N_c}$. We show that the large-$N_c$ derivation requires a momentum resolution scale of $\Lambda_{{\rm large-}N_c} \sim 500$ MeV. We derive a set of spin-isospin exchange sum rules and discuss implications for the spectrum of $^{30}$P and applications to nuclear forces, nuclear structure calculations, and three-nucleon interactions.Comment: 5 pages (main) + 3 pages (supplemental materials), 1 figure (main) + 4 figures (supplemental materials), final version to appear in Phys. Rev. Let