We present lattice calculations of the low-lying spectrum of $^{12}$C using a simple nucleon-nucleon interaction that is independent of spin and isospin and therefore invariant under Wigners SU(4) symmetry. We find strong signals for all excited stat
es up to $sim 15$~MeV above the ground state, and explore the structure of each state using a large variety of $alpha$ cluster and harmonic oscillator trial states, projected onto given irreducible representations of the cubic group. We are able to verify earlier findings for the $alpha$ clustering in the Hoyle state and the second $2^+$ state of $^{12}$C. The success of these calculations to describe the full low-lying energy spectrum using spin-independent interactions suggest that either the spin-orbit interactions are somewhat weak in the $^{12}$C system, or the effects of $alpha$ clustering are diminishing their influence. This is in agreement with previous findings from {it ab initio} shell model calculations.
We consider the problem of including $Lambda$ hyperons into the ab initio framework of nuclear lattice effective field theory. In order to avoid large sign oscillations in Monte Carlo simulations, we make use of the fact that the number of hyperons i
s typically small compared to the number of nucleons in the hypernuclei of interest. This allows us to use the impurity lattice Monte Carlo method, where the minority species of fermions in the full nuclear Hamiltonian is integrated out and treated as a worldline in Euclidean projection time. The majority fermions (nucleons) are treated as explicit degrees of freedom, with their mutual interactions described by auxiliary fields. This is the first application of the impurity lattice Monte Carlo method to systems where the majority particles are interacting. Here, we show how the impurity Monte Carlo method can be applied to compute the binding energy of the light hypernuclei. In this exploratory work we use spin-independent nucleon-nucleon and hyperon-nucleon interactions to test the computational power of the method. We find that the computational effort scales approximately linearly in the number of nucleons. The results are very promising for future studies of larger hypernuclear systems using chiral effective field theory and realistic hyperon-nucleon interactions, as well as applications to other quantum many-body systems.
The triple-alpha process, whereby evolved stars create carbon and oxygen, is believed to be fine-tuned to a high degree. Such fine-tuning is suggested by the unusually strong temperature dependence of the triple-alpha reaction rate at stellar tempera
tures. This sensitivity is due to the resonant character of the triple-alpha process, which proceeds through the so-called Hoyle state of $^{12}$C with spin-parity $0^+$. The question of fine-tuning can be studied within the {it ab initio} framework of nuclear lattice effective field theory, which makes it possible to relate {it ad hoc} changes in the energy of the Hoyle state to changes in the fundamental parameters of the nuclear Hamiltonian, which are the light quark mass $m_q$ and the electromagnetic fine-structure constant. Here, we update the effective field theory calculation of the sensitivity of the triple-alpha process to small changes in the fundamental parameters. In particular, we consider recent high-precision lattice QCD calculations of the nucleon axial coupling $g_A$, as well as new and more comprehensive results from stellar simulations of the production of carbon and oxygen. While the updated stellar simulations allow for much larger {it ad hoc} shifts in the Hoyle state energy than previously thought, recent lattice QCD results for the nucleon S-wave singlet and triplet scattering lengths now disfavor the scenario of no fine-tuning in the light quark mass $m_q$.
We explore the lattice spacing dependence in Nuclear Lattice Effective Field Theory for few-body systems up to next-to-next-to leading order in chiral effective field theory including all isospin breaking and electromagnetic effects, the complete two
-pion-exchange potential and the three-nucleon forces. We calculate phase shifts in the neutron-proton system and proton-proton systems as well as the scattering length in the neutron-neutron system. We then perform a full next-to-next-to-leading order calculation with two-nucleon and three-nucleon forces for the triton and helium-4 and analyse their binding energy correlation. We show how the Tjon band is reached by decreasing the lattice spacing and confirm the continuum observation that a four-body force is not necessary to describe light nuclei.
We introduce a general and accurate method for determining lattice phase shifts and mixing angles, which is applicable to arbitrary, non-cubic lattices. Our method combines angular momentum projection, spherical wall boundaries and an adjustable auxi
liary potential. This allows us to construct radial lattice wave functions and to determine phase shifts at arbitrary energies. For coupled partial waves, we use a complex-valued auxiliary potential that breaks time-reversal invariance. We benchmark our method using a system of two spin-1/2 particles interacting through a finite-range potential with a strong tensor component. We are able to extract phase shifts and mixing angles for all angular momenta and energies, with precision greater than that of extant methods. We discuss a wide range of applications from nuclear lattice simulations to optical lattice experiments.
We study the breaking of rotational symmetry on the lattice for irreducible tensor operators and practical methods for suppressing this breaking. We illustrate the features of the general problem using an $alpha$ cluster model for $^{8}$Be. We focus
on the lowest states with non-zero angular momentum and examine the matrix elements of multipole moment operators. We show that the physical reduced matrix element is well reproduced by averaging over all possible orientations of the quantum state, and this is expressed as a sum of matrix elements weighted by the corresponding Clebsch-Gordan coefficients. For our $alpha$ cluster model we find that the effects of rotational symmetry breaking can be largely eliminated for lattice spacings of $aleq 1.7$ fm, and we expect similar improvement for actual lattice Monte Carlo calculations.
Projection Monte Carlo calculations of lattice Chiral Effective Field Theory suffer from sign oscillations to a varying degree dependent on the number of protons and neutrons. Hence, such studies have hitherto been concentrated on nuclei with equal n
umbers of protons and neutrons, and especially on the alpha nuclei where the sign oscillations are smallest. Here, we introduce the symmetry-sign extrapolation method, which allows us to use the approximate Wigner SU(4) symmetry of the nuclear interaction to systematically extend the Projection Monte Carlo calculations to nuclear systems where the sign problem is severe. We benchmark this method by calculating the ground-state energies of the $^{12}$C, $^6$He and $^6$Be nuclei, and discuss its potential for studies of neutron-rich halo nuclei and asymmetric nuclear matter.
We explore the breaking of rotational symmetry on the lattice for bound state energies and practical methods for suppressing this breaking. We demonstrate the general problems associated with lattice discretization errors and finite-volume errors usi
ng an $alpha$ cluster model for $^8$Be and $^{12}$C. We consider the two and three $alpha$-particle systems and focus on the lowest states with non-zero angular momentum which split into multiplets corresponding to different irreducible representations of the cubic group. We examine the dependence of such splittings on the lattice spacing and box size. We find that lattice spacing errors are closely related to the commensurability of the lattice with the intrinsic length scales of the system. We also show that rotational symmetry breaking effects can be significantly reduced by using improved lattice actions, and that the physical energy levels are accurately reproduced by the weighted average of a given spin multiplets.
We present evidence, from Lattice Monte Carlo simulations of the phase diagram of graphene as a function of the Coulomb coupling between quasiparticles, that graphene in vacuum is likely to be an insulator. We find a semimetal-insulator transition at
$alpha_g^text{crit} = 1.11 pm 0.06$, where $alpha_g^{} simeq 2.16$ in vacuum, and $alpha_g^{} simeq 0.79$ on a SiO$_2^{}$ substrate. Our analysis uses the logarithmic derivative of the order parameter, supplemented by an equation of state. The insulating phase disappears above a critical number of four-component fermion flavors $4 < N_f^{text{crit}} < 6$. Our data are consistent with a second-order transition.
