arXiv subjects

Timo A. Lähde

Publications and source records attributed to Timo A. Lähde.

At least 37 records · Page 2Linked to original sources

arXiv2018

The Tjon Band in Nuclear Lattice Effective Field Theory

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.

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arXiv2017

Ab initio calculations of the isotopic dependence of nuclear clustering

Nuclear clustering describes the appearance of structures resembling smaller nuclei such as alpha particles (4He nuclei) within the interior of a larger nucleus. While clustering is important for several well-known examples, much remains to be discovered about the general nature of clustering in nuclei. In this letter we present lattice Monte Carlo calculations based on chiral effective field theory for the ground states of helium, beryllium, carbon, and oxygen isotopes. By computing model-independent measures that probe three- and four-nucleon correlations at short distances, we determine the shape of the alpha clusters and the entanglement of nucleons comprising each alpha cluster with the outside medium. We also introduce a new computational approach called the pinhole algorithm, which solves a long-standing deficiency of auxiliary-field Monte Carlo simulations in computing density correlations relative to the center of mass. We use the pinhole algorithm to determine the proton and neutron density distributions and the geometry of cluster correlations in 12C, 14C, and 16C. The structural similarities among the carbon isotopes suggest that 14C and 16C have excitations analogous to the well-known Hoyle state resonance in 12C.

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arXiv2017

Neutron-proton scattering at next-to-next-to-leading order in Nuclear Lattice Effective Field Theory

We present a systematic study of neutron-proton scattering in Nuclear Lattice Effective Field Theory (NLEFT), in terms of the computationally efficient radial Hamiltonian method. Our leading-order (LO) interaction consists of smeared, local contact terms and static one-pion exchange. We show results for a fully non-perturbative analysis up to next-to-next-to-leading order (NNLO), followed by a perturbative treatment of contributions beyond LO. The latter analysis anticipates practical Monte Carlo simulations of heavier nuclei. We explore how our results depend on the lattice spacing a, and estimate sources of uncertainty in the determination of the low-energy constants of the next-to-leading-order (NLO) two-nucleon force. We give results for lattice spacings ranging from a = 1.97 fm down to a = 0.98 fm, and discuss the effects of lattice artifacts on the scattering observables. At a = 0.98 fm, lattice artifacts appear small, and our NNLO results agree well with the Nijmegen partial-wave analysis for S-wave and P-wave channels. We expect the peripheral partial waves to be equally well described once the lattice momenta in the pion-nucleon coupling are taken to coincide with the continuum dispersion relation, and higher-order (N3LO) contributions are included. We stress that for center-of-mass momenta below 100 MeV, the physics of the two-nucleon system is independent of the lattice spacing.

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arXiv2016

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.

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arXiv2016

Precise determination of lattice phase shifts and mixing angles

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 auxiliary 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.

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arXiv2016

Quantum Monte Carlo Calculations for Carbon Nanotubes

We show how lattice Quantum Monte Carlo can be applied to the electronic properties of carbon nanotubes in the presence of strong electron-electron correlations. We employ the path-integral formalism and use methods developed within the lattice QCD community for our numerical work. Our lattice Hamiltonian is closely related to the hexagonal Hubbard model augmented by a long-range electron-electron interaction. We apply our method to the single-quasiparticle spectrum of the (3,3) armchair nanotube configuration, and consider the effects of strong electron-electron correlations. Our approach is equally applicable to other nanotubes, as well as to other carbon nanostructures. We benchmark our Monte Carlo calculations against the two- and four-site Hubbard models, where a direct numerical solution is feasible.

cond-mat.str-el↗

arXiv2015

Nuclear Lattice Simulations using Symmetry-Sign Extrapolation

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 numbers 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.

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arXiv2015

Ab initio alpha-alpha scattering

Processes involving alpha particles and alpha-like nuclei comprise a major part of stellar nucleosynthesis and hypothesized mechanisms for thermonuclear supernovae. In an effort towards understanding alpha processes from first principles, we describe in this letter the first ab initio calculation of alpha-alpha scattering. We use lattice effective field theory to describe the low-energy interactions of nucleons and apply a technique called the adiabatic projection method to reduce the eight-body system to an effective two-cluster system. We find good agreement between lattice results and experimental phase shifts for S-wave and D-wave scattering. The computational scaling with particle number suggests that alpha processes involving heavier nuclei are also within reach in the near future.

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arXiv2015

Breaking and restoration of rotational symmetry for irreducible tensor operators on the lattice

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 $α$ 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 $α$ cluster model we find that the effects of rotational symmetry breaking can be largely eliminated for lattice spacings of $a\leq 1.7$ fm, and we expect similar improvement for actual lattice Monte Carlo calculations.

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arXiv2014

Uncertainties of Euclidean Time Extrapolation in Lattice Effective Field Theory

Extrapolations in Euclidean time form a central part of Nuclear Lattice Effective Field Theory (NLEFT) calculations using the Projection Monte Carlo method, as the sign problem in many cases prevents simulations at large Euclidean time. We review the next-to-next-to-leading order NLEFT results for the alpha nuclei up to $^{28}$Si, with emphasis on the Euclidean time extrapolations, their expected accuracy and potential pitfalls. We also discuss possible avenues for improving the reliability of Euclidean time extrapolations in NLEFT.

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arXiv2014

Breaking and restoration of rotational symmetry on the lattice for bound state multiplets

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 using an $α$ cluster model for $^8$Be and $^{12}$C. We consider the two and three $α$-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.

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arXiv2014

Velocity renormalization in graphene from lattice Monte Carlo

We compute the Fermi velocity of the Dirac quasiparticles in clean graphene at the charge neutrality point for strong Coulomb coupling alpha_g. We perform a Lattice Monte Carlo calculation within the low-energy Dirac theory, which includes an instantaneous, long-range Coulomb interaction. We find a renormalized Fermi velocity v_FR > v_F, where v_F = c/300. Our results are consistent with a momentum-independent v_FR which increases approximately linearly with alpha_g, although a logarithmic running with momentum cannot be excluded at present. At the predicted critical coupling alpha_gc for the semimetal-insulator transition due to excitonic pair formation, we find v_FR/v_F = 3.3, which we discuss in light of experimental findings for v_FR/v_F at the charge neutrality point in ultra-clean suspended graphene.

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arXiv2014

The Hoyle state in Nuclear Lattice EFT

We review the calculation of the Hoyle state of $^{12}$C in Nuclear Lattice Effective Field Theory (NLEFT) and its anthropic implications for the nucleosynthesis of $^{12}$C and $^{16}$O in red giant stars. We also review the extension of NLEFT to the regime of medium-mass nuclei, with emphasis on the determination of the ground-state energies of the alpha nuclei $^{16}$O, $^{20}$Ne, $^{24}$Mg and $^{28}$Si by means of Euclidean time projection. Finally, we review recent NLEFT results for the spectrum, electromagnetic properties, and alpha-cluster structure of $^{16}$O.

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arXiv2014

Lattice Effective Field Theory for Medium-Mass Nuclei

We extend Nuclear Lattice Effective Field Theory (NLEFT) to medium-mass nuclei, and present results for the ground states of alpha nuclei from $^4$He to $^{28}$Si, calculated up to next-to-next-to-leading order (NNLO) in the EFT expansion. This computational advance is made possible by extrapolations of lattice data using multiple initial and final states. For our soft two-nucleon interaction, we find that the overall contribution from multi-nucleon forces must change sign from attractive to repulsive with increasing nucleon number. This effect is not produced by three-nucleon forces at NNLO, but it can be approximated by an effective four-nucleon interaction. We discuss the convergence of the EFT expansion and the broad significance of our findings for future ab initio calculations.

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arXiv2014

Ab initio calculation of the spectrum and structure of $^{16}$O

We present ab initio lattice calculations of the low-energy even-parity states of $^{16}$O using chiral nuclear effective field theory. We find good agreement with the empirical energy spectrum, and with the electromagnetic properties and transition rates. For the ground state, we find that the nucleons are arranged in a tetrahedral configuration of alpha clusters. For the first excited spin-0 state, we find that the predominant structure is a square configuration of alpha clusters, with rotational excitations that include the first spin-2 state.

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arXiv2013

Two-loop Sunset Integrals at Finite Volume

We show how to compute the two-loop sunset integrals at finite volume, for non-degenerate masses and non-zero momentum. We present results for all integrals that appear in the Chiral Perturbation Therory ($χ$PT) calculation of the pseudoscalar meson masses and decay constants at NNLO, including the case of Partially Quenched $χ$PT. We also provide numerical implementations of the finite-volume sunset integrals, and review the results for one-loop integrals at finite volume.

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arXiv2013

Lattice effective field theory for nuclei from A = 4 to A = 28

We present an overview of the extension of Nuclear Lattice Effective Field Theory simulations to the regime of medium-mass nuclei. We focus on the determination of the ground-state energies of the alpha nuclei $^{16}$O, $^{20}$Ne, $^{24}$Mg and $^{28}$Si by means of Euclidean time projection.

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arXiv2013

Dependence of the triple-alpha process on the fundamental constants of nature

We present an ab initio calculation of the quark mass dependence of the ground state energies of ^4He, ^8Be and ^{12}C, and of the energy of the Hoyle state in ^{12}C. These investigations are performed within the framework of lattice chiral Effective Field Theory. We address the sensitivity of the production rate of carbon and oxygen in red giant stars to the fundamental constants of nature by considering the impact of variations in the light quark masses and the electromagnetic fine-structure constant on the reaction rate of the triple-alpha process. As carbon and oxygen are essential to life as we know it, we also discuss the implications of our findings for an anthropic view of the Universe. We find strong evidence that the physics of the triple-alpha process is driven by alpha clustering, and that shifts in the fundamental parameters at the \simeq 2 - 3 % level are unlikely to be detrimental to the development of life. Tolerance against much larger changes cannot be ruled out at present, given the relatively limited knowledge of the quark mass dependence of the two-nucleon S-wave scattering parameters. Lattice QCD is expected to provide refined estimates of the scattering parameters in the future.

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