arXiv subjects

Timo A. Lähde

Publications and source records attributed to Timo A. Lähde.

At least 19 recordsLinked to original sources

arXiv2026

Nuclear lattice effective field theory as a testing ground for $α$-cluster structures in ${}^{24}\mathrm{Mg}$

The framework of nuclear lattice effective field theory (NLEFT) is applied to $^{24}\mathrm{Mg}$, with the perspective of obtaining a model-independent density map of the geometry of a sample of excited states of the nucleus. The Hamiltonian incorporates Wigner SU(4)-symmetric nuclear forces as well as the Coulomb interaction. The coupling constants of the spin-isospin symmetric nucleon-nucleon potentials have been adjusted in order to reproduce the experimental ground-state (g.s.) energy of $^{24}\mathrm{Mg}$ as well as the experimental Tjon ratio between the binding energies of $^3\mathrm{H}$ and $^4\mathrm{He}$. The ensuing parameter set turns out to be capable of capturing the experimental trend of the binding energy per nucleon, reproducing simultaneously within 1% deviation the measured values for $^{18}\mathrm{F}$, $^{22}\mathrm{Na}$, $^{26}\mathrm{Al}$, $^{28}\mathrm{Si}$, $^{30}\mathrm{P}$ and $^{32}\mathrm{S}$. Considerations based on the convergence rate of Euclidean-time extrapolations for the two lowest energy eigenvalues highlight the dual nature of the $0_1^+$ and $2_1^+$ states, of hybrid mean-field and $α$-cluster type. For the latter, triaxial $α$-cluster configurations seem to be favoured over the axially-symmetric ones, whereas oblate superdeformation might characterize a rotational band at $20$ MeV excitation energy.

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arXiv2026

Ab initio $α$-$α$ scattering with high-fidelity chiral interactions

Low-energy $α$-$α$ scattering underlies stellar helium burning and sharply tests nuclear forces in the reaction regime. We present its first calculation using the high-fidelity N3LO chiral NLEFT interaction, incorporated through wave function matching, on a fine lattice, using the adiabatic projection method. On the fine lattice, the two-cluster norm matrix becomes severely ill-conditioned, and its direct inversion is unstable. We address this with Tikhonov regularization, extrapolating the regulator to zero, and confirm the result with an independent truncated singular-value decomposition. The S- and D-wave phase shifts agree with empirical analyses, extending the validation of this interaction from bound states and charge radii to scattering and providing a practical route to ab initio nuclear reactions on fine lattices

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arXiv2025

Anisotropic flow in fixed-target $^{208}$Pb+$^{20}$Ne collisions as a probe of quark-gluon plasma

The System for Measuring Overlap with Gas (SMOG2) at the LHCb detector enables the study of fixed-target ion-ion collisions at relativistic energies ($\sqrt{s_{\rm NN}}\sim100$ GeV in the centre-of-mass). With input from \textit{ab initio} calculations of the structure of $^{16}$O and $^{20}$Ne, we compute 3+1D hydrodynamic predictions for the anisotropic flow of Pb+Ne and Pb+O collisions, to be tested with upcoming LHCb data. This will allow the detailed study of quark-gluon plasma (QGP) formation as well as experimental tests of the predicted nuclear shapes. Elliptic flow ($v_2$) in Pb+Ne collisions is greatly enhanced compared to the Pb+O baseline due to the shape of $^{20}$Ne, which is deformed in a bowling-pin geometry. Owing to the large $^{208}$Pb radius, this effect is seen in a broad centrality range, a unique feature of this collision configuration. Larger elliptic flow further enhances the quadrangular flow ($v_4$) of Pb+Ne collisions via non-linear coupling, and impacts the sign of the kurtosis of the elliptic flow vector distribution ($c_2\{4\}$). Exploiting the shape of $^{20}$Ne proves thus an ideal method to investigate the formation of QGP in fixed-target experiments at LHCb, and demonstrates the power of SMOG2 as a tool to image nuclear ground states.

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arXiv2024

Wavefunction matching for solving quantum many-body problems

Ab initio calculations play an essential role in our fundamental understanding of quantum many-body systems across many subfields, from strongly correlated fermions to quantum chemistry and from atomic and molecular systems to nuclear physics. One of the primary challenges is to perform accurate calculations for systems where the interactions may be complicated and difficult for the chosen computational method to handle. Here we address the problem by introducing a new approach called wavefunction matching. Wavefunction matching transforms the interaction between particles so that the wavefunctions up to some finite range match that of an easily computable interaction. This allows for calculations of systems that would otherwise be impossible due to problems such as Monte Carlo sign cancellations. We apply the method to lattice Monte Carlo simulations of light nuclei, medium-mass nuclei, neutron matter, and nuclear matter. We use high-fidelity chiral effective field theory interactions and find good agreement with empirical data. These results are accompanied by new insights on the nuclear interactions that may help to resolve long-standing challenges in accurately reproducing nuclear binding energies, charge radii, and nuclear matter saturation in ab initio calculations.

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arXiv2024

The unexpected uses of a bowling pin: exploiting $^{20}$Ne isotopes for precision characterizations of collectivity in small systems

Whether or not femto-scale droplets of quark-gluon plasma (QGP) are formed in so-called small systems at high-energy colliders is a pressing question in the phenomenology of the strong interaction. For proton-proton or proton-nucleus collisions the answer is inconclusive due to the large theoretical uncertainties plaguing the description of these processes. While upcoming data on collisions of $^{16}$O nuclei may mitigate these uncertainties in the near future, here we demonstrate the unique possibilities offered by complementing $^{16}$O$^{16}$O data with collisions of $^{20}$Ne ions. We couple both NLEFT and PGCM ab initio descriptions of the structure of $^{20}$Ne and $^{16}$O to hydrodynamic simulations of $^{16}$O$^{16}$O and $^{20}$Ne$^{20}$Ne collisions at high energy. We isolate the imprints of the bowling-pin shape of $^{20}$Ne on the collective flow of hadrons, which can be used to perform quantitative tests of the hydrodynamic QGP paradigm. In particular, we predict that the elliptic flow of $^{20}$Ne$^{20}$Ne collisions is enhanced by as much as 1.170(8)$_{\rm stat.}$(30)$_{\rm syst.}$ for NLEFT and 1.139(6)$_{\rm stat.}$(39)$_{\rm syst.}$ for PGCM relative to $^{16}$O$^{16}$O collisions for the 1% most central events. At the same time, theoretical uncertainties largely cancel when studying relative variations of observables between two systems. This demonstrates a method based on experiments with two light-ion species for precision characterizations of the collective dynamics and its emergence in a small system.

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arXiv2023

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.

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arXiv2023

Emergent geometry and duality in the carbon nucleus

The carbon atom provides the backbone for the complex organic chemistry composing the building blocks of life. The physics of the carbon nucleus in its predominant isotope, $^{12}$C, is similarly full of multifaceted complexity. Some nuclear states of $^{12}$C can be preferentially treated as a collection of independent particles held by the mean field of the nucleus, while other states behave more as a collection of three alpha-particle clusters. But these two pictures are not mutually exclusive, and some states can be described in either fashion$^{1,2}$. In this work, we provide the first model-independent tomographic scan of the three-dimensional geometry of the nuclear states of $^{12}$C using the {\it ab initio} framework of nuclear lattice effective field theory. We find that the well-known but enigmatic Hoyle state is composed of a "bent-arm" or obtuse triangular arrangement of alpha clusters. We identify all of the low-lying nuclear states of $^{12}$C as having an intrinsic shape composed of three alpha clusters forming either an equilateral triangle or an obtuse triangle. From these basic structural formations, the various nuclear states correspond to different rotational and vibrational excitations as well as either distortions or large-amplitude displacements of the alpha clusters. The states with the equilateral triangle formation also have a dual description in terms of particle-hole excitations in the mean-field picture. We compare our theoretical calculations with experimental data for binding energies, quadrupole moments, electromagnetic transitions, charge densities, and form factors. The overall agreement is good, and further studies using higher-fidelity interactions are planned.

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arXiv2022

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.

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arXiv2021

Alpha-alpha scattering in the Multiverse

We investigate the phase shifts of low-energy alpha-alpha scattering under variations of the fundamental parameters of the Standard Model, namely the light quark mass, the electromagnetic fine-structure constant as well as the QCD theta-angle. As a first step, we recalculate alpha-alpha scattering in our Universe utilizing various improvements in the adiabatic projection method, which leads to an improved, parameter-free prediction of the S- and D-wave phase shifts for laboratory energies below 10 MeV. We find that positive shifts in the pion mass have a small effect on the S-wave phase shift, whereas lowering the pion mass adds some repulsion in the two-alpha system. The effect on the D-wave phase shift turns out to be more pronounced as signaled by the D-wave resonance parameters. Variations of the fine-structure constant have almost no effect on the low-energy alpha-alpha phase shifts. We further show that up-to-and-including next-to-leading order in the chiral expansion, variations of these phase shifts with respect to the QCD theta-angle can be expressed in terms of the theta-dependent pion mass.

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arXiv2021

Ab initio nuclear thermodynamics from lattice effective field theory

We show that the {\it ab initio} calculations of nuclear thermodynamics can be performed efficiently using lattice effective field theory. The simulations use a new approach called the pinhole trace algorithm to calculate thermodynamic observables for a fixed number of protons and neutrons enclosed in a finite box. In this framework, we calculate the equation of state, the liquid-vapor coexistence line and the critical point of neutral symmetric nuclear matter with high precision. Since the algorithm uses a canonical ensemble with a fixed number of particles, it provides a sizable computational advantage over grand canonical ensemble simulations that can be a factor of several thousands to as much as several millions for large volume simulations.

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arXiv2021

The Antiferromagnetic Character of the Quantum Phase Transition in the Hubbard Model on the Honeycomb Lattice

We provide a unified, comprehensive treatment of all operators that contribute to the anti-ferromagnetic, ferromagnetic, and charge-density-wave structure factors and order parameters of the hexagonal Hubbard Model. We use the Hybrid Monte Carlo algorithm to perform a systematic, carefully controlled analysis in the temporal Trotter error and of the thermodynamic limit. We expect our findings to improve the consistency of Monte Carlo determinations of critical exponents. We perform a data collapse analysis and determine the critical exponent $β=0.898(37)$ for the semimetal-Mott insulator transition in the hexagonal Hubbard Model. Our methods are applicable to a wide range of lattice theories of strongly correlated electrons.

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arXiv2021

The Semimetal-Antiferromagnetic Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice

The Hubbard model on the honeycomb lattice undergoes a quantum phase transition from a semimetallic to a Mott insulating phase and from a disordered to an anti-ferromagnetically phase. We show that these transitions occur simultaneously and we calculate the critical coupling $U_c=3.835(14)$ as well as the critical exponents $ν=1.181(43)$ and $β=0.898(37)$ which are expected to fall into the $SU(2)$ Gross-Neveu universality class. For this we employ Hybrid Monte Carlo simulations, extrapolate the single particle gap and the spin structure factors to the thermodynamic and continuous time limits, and perform a data collapse fit. We also determine the zero temperature values of single particle gap and staggered magnetisation on both sides of the phase transition.

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arXiv2021

Wigner SU(4) symmetry, clustering, and the spectrum of $^{12}$C

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 Wigner's SU(4) symmetry. We find strong signals for all excited states up to $\sim 15$~MeV above the ground state, and explore the structure of each state using a large variety of $α$ cluster and harmonic oscillator trial states, projected onto given irreducible representations of the cubic group. We are able to verify earlier findings for the $α$ 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 $α$ clustering are diminishing their influence. This is in agreement with previous findings from {\it ab initio} shell model calculations.

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arXiv2020

The Semimetal-Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice

We take advantage of recent improvements in the grand canonical Hybrid Monte Carlo algorithm, to perform a precision study of the single-particle gap in the hexagonal Hubbard model, with on-site electron-electron interactions. After carefully controlled analyses of the Trotter error, the thermodynamic limit, and finite-size scaling with inverse temperature, we find a critical coupling of $U_c/κ=3.834(14)$ and the critical exponent $zν=1.185(43)$. Under the assumption that this corresponds to the expected anti-ferromagnetic Mott transition, we are also able to provide a preliminary estimate $β=1.095(37)$ for the critical exponent of the order parameter. We consider our findings in view of the $SU(2)$ Gross-Neveu, or chiral Heisenberg, universality class. We also discuss the computational scaling of the Hybrid Monte Carlo algorithm, and possible extensions of our work to carbon nanotubes, fullerenes, and topological insulators.

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arXiv2020

Impurity Lattice Monte Carlo for Hypernuclei

We consider the problem of including $Λ$ 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 is 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.

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arXiv2020

Ab initio nuclear thermodynamics

We propose a new Monte Carlo method called the pinhole trace algorithm for {\it ab initio} calculations of the thermodynamics of nuclear systems. For typical simulations of interest, the computational speedup relative to conventional grand-canonical ensemble calculations can be as large as a factor of one thousand. Using a leading-order effective interaction that reproduces the properties of many atomic nuclei and neutron matter to a few percent accuracy, we determine the location of the critical point and the liquid-vapor coexistence line for symmetric nuclear matter with equal numbers of protons and neutrons. We also present the first {\it ab initio} study of the density and temperature dependence of nuclear clustering.

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arXiv2020

Avoiding Ergodicity Problems in Lattice Discretizations of the Hubbard Model

The Hubbard model arises naturally when electron-electron interactions are added to the tight-binding descriptions of many condensed matter systems. For instance, the two-dimensional Hubbard model on the honeycomb lattice is central to the ab initio description of the electronic structure of carbon nanomaterials, such as graphene. Such low-dimensional Hubbard models are advantageously studied with Markov chain Monte Carlo methods, such as Hybrid Monte Carlo (HMC). HMC is the standard algorithm of the lattice gauge theory community, as it is well suited to theories of dynamical fermions. As HMC performs continuous, global updates of the lattice degrees of freedom, it provides superior scaling with system size relative to local updating methods. A potential drawback of HMC is its susceptibility to ergodicity problems due to so-called exceptional configurations, for which the fermion operator cannot be inverted. Recently, ergodicity problems were found in some formulations of HMC simulations of the Hubbard model. Here, we address this issue directly and clarify under what conditions ergodicity is maintained or violated in HMC simulations of the Hubbard model. We study different lattice formulations of the fermion operator and provide explicit, representative calculations for small systems, often comparing to exact results. We show that a fermion operator can be found which is both computationally convenient and free of ergodicity problems.

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arXiv2019

An update on fine-tunings in the triple-alpha process

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 temperatures. 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 $m_q$.

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