Dense nucleonic matter is of vital importance for understanding compact stars and inferring the transition into deconfined quark phase. We present ab initio exact calculations of infinite nucleonic matter with the state-of-the-art full configuration-interaction quantum Monte Carlo method, enabling us to rigorously benchmark many-body methods and assess the degree to which the nucleonic matter is correlated. Our method has been numerically validated against exact diagonalization within a small model space. Calculations of nucleonic matter using chiral nuclear forces reveal that symmetric nuclear matter is strikingly strongly correlated, raising questions on previous ab initio calculations of nuclear matter with many-body expansion truncations and offering insights into simultaneous descriptions of finite nuclei and infinite nucleonic matter from first principles.
Dense nucleonic matter is of vital importance for understanding compact stars and inferring the transition into deconfined quark phase. We present ab initio exact calculations of infinite nucleonic matter with the state-of-the-art full configuration-interaction quantum Monte Carlo method, enabling us to rigorously benchmark many-body methods and assess the degree to which the nucleonic matter is correlated. Our method has been numerically validated against exact diagonalization within a small model space. Calculations of nucleonic matter using chiral nuclear forces reveal that symmetric nuclear matter is strikingly strongly correlated, raising questions on previous ab initio calculations of nuclear matter with many-body expansion truncations and offering insights into simultaneous descriptions of finite nuclei and infinite nucleonic matter from first principles.
Full Configuration Interaction Quantum Monte Carlo for Accurate Ab Initio Nuclear Structure Calculations
We introduce novel full configuration interaction quantum Monte Carlo (FCIQMC) as an accurate many-body solver for ab initio nuclear structure calculations. This stochastic approach directly samples the exact wave function in the full configuration space, enabling high-fidelity treatment of high-order many-body correlations in strongly interacting nuclear systems. Using interactions from chiral effective field theory, we have computed ground-state energies and charge radii of 4He, 8Be, 12C and 16O with sub-percent-level many-body uncertainties. These results establish FCIQMC as a stochastic full-configuration-space solver capable of treating systems beyond the reach of the conventional no-core shell model, and as an accurate benchmark for truncated many-body expansion methods.
Full configuration interaction quantum Monte Carlo for accurate ab initio nuclear structure calculations: algorithms and calculation details
Full configuration interaction quantum Monte Carlo (FCIQMC) is a stochastic many-body solver that has been widely applied to electronic, molecular, and condensed-matter systems. In this work we apply FCIQMC to ab initio nuclear structure calculations using interactions derived from chiral effective field theory. We describe the algorithm in detail, including imaginary-time propagation, excitation generation, estimator choices, the initiator approximation with adaptive shift correction, and reduced-density-matrix (RDM) sampling. Benchmark calculations in small model spaces, where deterministic full configuration interaction (FCI) results are available, validate the stochastic calculation of energies, radii, and RDM-based pure estimators. For large model spaces, we analyze the residual finite-walker bias through systematic walker-number convergence and infinite-walker extrapolations. We also demonstrate that FCIQMC can be extended beyond ground-state calculations by computing the low-lying spectrum of 6Li.
Abstract Ab initio calculations have an essential role in our fundamental understanding of quantum many-body systems across many subfields, from strongly correlated fermions 1–3 to quantum chemistry 4–6 and from atomic and molecular systems 7–9 to nuclear physics 10–14 . 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 an 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 owing to problems such as Monte Carlo sign cancellations. We apply the method to lattice Monte Carlo simulations 15,16 of light nuclei, medium-mass nuclei, neutron matter and nuclear matter. We use high-fidelity chiral effective field theory interactions 17,18 and find good agreement with empirical data. These results are accompanied by 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 19,20 .
Neutron matter, through its connection to neutron stars as well as systems such as cold atom gases, is one of the most interesting yet computationally accessible systems in nuclear physics. The configuration-interaction Monte Carlo (CIMC) method is a stochastic many-body technique allowing us to tackle strongly coupled systems. In contrast to other quantum Monte Carlo methods employed in nuclear physics, the CIMC method can be formulated directly in momentum space allowing for an efficient use of nonlocal interactions. In this work we extend CIMC method to include three-nucleon interactions through the normal-ordered two-body approximation. We present results for the equation of state of neutron matter in line with other many-body calculations that employ low-resolution chiral interactions, and provide predictions for the momentum distribution and the static structure factor.
The shell model provides a powerful framework for nuclear structure calculations. The nucleons beyond an inert magic core are confined in a valence shell and interact through an effective two-body potential generally determined from the G-matrix method. However, the applicability of the shell model remains limited by the exponential growth of the many-body space with the number of valence nucleons and with the size of the one-body space. The quantum Monte Carlo (QMC) methods may thus be considered as a potentially attractive alternative to the direct diagonalization of the Hamiltonian matrix. The many-body problem is indeed reduced to a set of stochastic one-body problems describing independent particles in a fluctuating external field. Up to date, the QMC approaches of the shell model lead to the ground-state and the thermodynamic properties, but a detailed spectroscopy of nuclei is not reachable. Furthermore, they suffer from a common pathology of fermionic QMC methods, namely the sign/phase problem, which strongly contaminates the convergence of the calculation. In this context, we will present a new QMC method, providing the "yrast spectroscopy" of nuclei, and in which the sign/phase problem is managed through the constrained path approximation that is widely used in the ab initio nuclear calculations and in condensed matter physics.
A long-standing goal of nuclear theory is to explain how the structure and dynamics of atomic nuclei and neutron-star matter emerge from the underlying interactions among protons and neutrons. Achieving this goal requires solving the nuclear quantum many-body problem with high accuracy across a wide range of length scales and density regimes. In this review, we discuss how artificial neural network representations of the nuclear many-body wave function have significantly extended the capabilities of continuum quantum Monte Carlo methods. In particular, neural network quantum states enable calculations of larger systems than were previously accessible and provide a flexible framework for capturing phenomena that challenge conventional approaches, including the emergence of nuclear clusters and superfluid phases in dense matter. We highlight recent applications to finite nuclei, infinite nuclear and neutron matter, and dynamical processes relevant to lepton-nucleus and nucleus-nucleus scattering. We also discuss conceptual and methodological connections with condensed matter physics, emphasizing developments in neural network quantum states that bridge strongly correlated systems across disciplines. Together, these developments demonstrate how neural-network methods open new avenues toward unified and accurate descriptions of nuclear structure, matter, and reactions.