arXiv subjects

Bing-Nan Lu

Publications and source records attributed to Bing-Nan Lu.

At least 19 recordsLinked to original sources

arXiv2026

Machine Learning Unveils Finite-volume Energy Shifts in Three-body System

Finite-volume extrapolation (FVE) is essential for extracting physical observables in the lattice calculation. While rigorous FVE formulations are well established for short-range potentials in both two- and three-body systems, long-range interactions with force ranges comparable to the lattice size $L$ remain challenging. Extending a previous data-driven scheme for two-body systems, we apply symbolic regression (PySR) to uncover universal three-body FVE formulae. For short-range potentials, we reproduce the two limiting cases, i.e. $κ_3\ggκ_2$ and $κ_3\simκ_2$. For pure long-range potentials, we obtain a dedicated analytic expression, and after incorporating short-range contributions, we uncover a unified formula consistent with the original PySR solution, which performs excellently in the intermediate force range around 1 fm. This work demonstrates that combining machine learning with physical constraints can yield novel analytical results inaccessible to conventional theoretical tools, advancing data-driven methodologies in hadron physics.

hep-lat↗

arXiv2026

Multi-reference Trial State for Lattice Quantum Monte Carlo Simulations

Nuclear lattice effective field theory (NLEFT) is an efficient \textit{ab initio} tool for solving nuclear many-body systems using the imaginary-time projection technique, where the preparation of trial states is essential for substantially reducing the computational cost required to achieve the desired numerical precision. It has been challenging in forming optimal multi-reference trial states using multiple Slater determinants within auxiliary-field based quantum Monte Carlo frameworks like NLEFT. In this work, we develop a novel sampling method for efficiently incorporating such multi-reference trial states into NLEFT calculations. We applied the optimized trial state to $^7$Li and $^8$Li, finding overall improvements in calculated energies, electromagnetic properties, and transitions compared to results obtained without these optimizations. Our approach provides a reliable foundation for accurately simulating nuclear ground and low-lying excited states within the NLEFT framework.

nucl-th↗

arXiv2026

Observation of renormalization group invariance in symmetry-restored nuclear lattice effective field theory

Renormalization group (RG) invariance implies that the predictions of effective field theory are independent of the momentum cutoffs introduced during regularization. Here we report the first systematic verification of RG invariance for realistic nuclear few-body systems within nuclear lattice effective field theory. To restore broken continuum rotational and Galilean symmetries, we employ Galilean-invariance-restoration counterterms and use a soft momentum regulator. We calibrate the two- and three-body next-to-next-to leading order (N$^2$LO) chiral forces using $A\leq 3$ observables and perform precision quantum Monte Carlo calculations to compute the $^4$He binding energy. The predicted energy remains constant across cutoffs from $250$~MeV to $400$~MeV and agrees well with the experimental value, with discrepancies of order 100 keV. Our results demonstrate the capability of extracting accurate, cutoff-independent predictions within lattice-regulated \textit{ab initio} nuclear theory.

nucl-th↗

arXiv2026

Dilated coordinate method for solving nuclear lattice effective field theory

We introduce a dilated coordinate method to address computational challenges in nuclear lattice effective field theory (NLEFT) for weakly-bound few-body systems. The approach employs adaptive mesh refinement via analytic coordinate transformations, dynamically adjusting spatial resolution to resolve short-range nuclear interactions with fine grids while efficiently capturing long-range wave function tails with coarse grids. Numerical demonstrations for two- and three-body systems confirm accelerated convergence towards infinite-volume limit compared to uniform lattices, particularly beneficial for accessing highly excited states and shallow bound states near the continuum threshold. This method establishes a foundation for \textit{ab initio} studies of exotic nuclear systems near the dripline and light hypernuclei, with direct extensions to scattering and reaction processes.

nucl-th↗

arXiv2026

Ab initio lattice calculation of nuclear magnetic dipole moments with systematic error quantifications

Nuclear magnetic moments are sensitive probes of nuclear structure. However, their accurate quantitative description poses significant challenges, demanding both accurate nuclear and electromagnetic interactions as well as rigorous control of algorithmic uncertainties. Here, we present the first systematic calculation of magnetic dipole moments for selected light nuclei and aluminum isotopes within nuclear lattice effective field theory (NLEFT), an \textit{ab initio} framework applicable to medium-mass and heavy nuclei. Our calculations employ a lattice next-to-next-to-next-to-leading-order (N$^3$LO) chiral interaction together with electromagnetic currents consistently derived up to the two-body level. To achieve controlled predictions, we incorporate recently developed NLEFT algorithms and perform a comprehensive assessment of algorithmic uncertainties. Within the estimated uncertainties, our results are in good overall agreement with experiment and demonstrate that two-body currents are essential for reproducing the observed magnetic moments. We further benchmark our predictions against other \textit{ab initio} calculations for light nuclei ($A\leq12$). Our work establishes a solid foundation for \textit{ab initio} studies of electroweak observables using methods that scale efficiently to medium-mass and heavy nuclei while demonstrating state-of-the-art accuracy.

nucl-th↗

arXiv2026

The anomalous long lifetime of $^{14}$C revealed by ab initio nuclear lattice EFT

The 5730-year half-life of $^{14}$C, the physical basis of radiocarbon dating, is anomalously long compared to typical nuclear-physics expectations. Its origin has remained a subject of debate for many decades. Here we report an \textit{ab initio} nuclear lattice effective field theory (NLEFT) calculation of $^{14}$C $β$ decay. Using systematically optimized interactions and transition operators consistently derived from chiral effective field theory, We obtain a result consistent with the Gamow-Teller matrix element $M_\text{GT}^\text{exp}\simeq 2\times 10^{-3}$ measured with the current uncertainty of $O(10^{-2})$. We first show that chiral interactions and weak currents beyond leading-order are essential for quenching the GT matrix element to the physical value, among which the optimization of three-nucleon forces is indispensable. We then illustrate that the quenching is deeply rooted in the ground-state structure of $^{14}$N as found in the nuclear shell model, where the competition between $S$- and $D$-wave components exists, sensitive to the interaction employed. The physical $^{14}$N ground state is found to be dominated by $D$-wave configurations, which constitutes the key factor for the quenching. The sensitivity of the decay matrix element to the fine-tuning of low-energy-constants is explored, revealing the prominent role of the $^3S_1$-channel two-nucleon contact force and the one-pion-exchange three-nucleon force. This work eliminates the gap between shell-model and \textit{ab initio} studies of $^{14}$C $β$ decay, provides a valid and straightforward explanation for the anomalous long lifetime of $^{14}$C, and turns NLEFT into a practical tool for the systematic study of nuclear transitions.

nucl-th↗

arXiv2026

Full Uncertainty Quantification of Sign-Problem-Free Quantum Monte Carlo Methods and Nuclear Lattice Effective Field Theory Benchmarks

Sign-problem-free quantum Monte Carlo (QMC) methods provide one of the few polynomial-scaling routes to controlled, nonperturbative benchmarks of medium-mass and heavy nuclei. We present a detailed uncertainty analysis of the recently developed sign-problem-free spin-orbit lattice action LAT-OPT1 and use it to benchmark nuclear lattice effective field theory (NLEFT). We quantify various systematic uncertainties, finding that the cumulative many-body computational uncertainty in ground-state energies of doubly magic nuclei up to $^{100}$Sn is well below the percent level. In response to recent criticism of NLEFT benchmarks, we also revisit the relation between lattice transfer matrices, lattice Hamiltonians, Hartree--Fock variational bounds, finite-box and thermodynamic-limit calculations, and the continuum-limit behavior of regulated lattice interactions. We identify several conceptual and technical errors in the analysis of Ref.~\cite{Rothman2026_NuLattice}. These include (i) the comparison of inequivalent lattice transfer-matrix and lattice-Hamiltonian calculations, (ii) an inconsistent determination of correlation energies from comparisons of Hartree--Fock and full ground-state calculations with different boundary conditions, (iii) the attribution of nuclear saturation to lattice artifacts rather than to nonlocal smearing of interactions, a mechanism that can be demonstrated in continuous space, and (iv) an incorrect renormalization of short-range two-body interactions in the continuum limit. When the same regulated lattice theory, renormalization prescription, and finite-volume boundary conditions are used consistently and analyzed properly, the reported discrepancies and concerns about the corresponding published NLEFT results are resolved.

nucl-th↗

arXiv2026

Neural-network excited states of $A=4$ nuclei and hypernuclei

We present the first variational Monte Carlo study of nuclear and hypernuclear excited states within the neural-network quantum states (NQS) framework. We implement both the overlap penalty (OP) and natural excited state (NES) methods to compute low-lying excitation spectra. To address the spin contamination in hypernuclear calculations, we propose a quantum number targeting (QNT) technique for the OP method. Both the OP-QNT and NES methods can reproduce diagonal observables, such as energies and spatial structures, in excellent agreement with rigorous benchmarks. We further provide, to our knowledge, the first \textit{ab initio} calculation of the $M1$ transition strength for $^{4}_Λ\mathrm{H}$. The calculated transition strength is consistent with the weak-coupling limit, exhibiting a $\sim$1.3\% suppression. This work demonstrates that NQS can be elevated from ground-state solvers to practical tools for nuclear and hypernuclear spectroscopy.

nucl-th↗

arXiv2026

Cutoff-independent predictions from nuclear lattice effective field theory

Cutoff independence is an essential requirement for the predictive power of nuclear \textit{ab initio} calculations based on effective field theory (EFT). While it is conventionally assumed that such invariance necessitates high-order interactions and complex many-body forces, we present a minimal chiral nuclear force that exhibits remarkable cutoff independence across a broad range from light to medium-mass nuclei and sub-saturated nuclear matter. Our framework comprises only contact terms up to next-to-leading order, a single three-nucleon contact force, and a leading-order one-pion-exchange potential, all constrained strictly in the $A \leq 3$ sector. Despite its simplicity, this interaction accurately reproduces experimental binding energies up to $^{40}\text{Ca}$ with unexpectedly small residual cutoff dependencies of only a few MeV. We demonstrate that the use of a lattice-inspired \emph{absolute}-momentum regulator efficiently suppresses high-momentum modes, resolving the overbinding problem for soft chiral forces without invoking complex many-body forces. These results establish a robust and economic foundation for EFT-based \textit{ab initio} calculations in both continuum and lattice frameworks.

nucl-th↗

arXiv2026

Quantum computing for effective nuclear lattice model

Nuclear lattice effective field theory has become an important framework for quantum many-body calculations in nuclear physics, yet its classical implementation remains increasingly challenging for more general interactions and larger systems. In this work, we develop a quantum-computing framework for a three-dimensional nuclear lattice model. We construct a variational quantum eigensolver framework and systematically compare the Jordan-Wigner and Gray code encodings. Our analysis shows that for the few-body systems considered here, Gray code combined with symmetry reduction yields a substantially more compact qubit representation. Based on this framework, we perform numerical studies for $^{2}\mathrm{H}$, $^{3}\mathrm{H}$, and $^{4}\mathrm{He}$ on finite lattices. The calculated ground-state energies exhibit a clear approach toward the corresponding experimental binding energies as the lattice size increases. These results provide a proof-of-principle foundation for future quantum simulations of nuclear many-body problems.

quant-ph↗

arXiv2026

Extracting Resonance Width from Lattice Quantum Monte Carlo Simulations Using Analytical Continuation Method

Nuclear lattice effective field theory (NLEFT) provides an efficient ab initio framework for computing low-lying states via imaginary-time projection. However, the extraction of unstable resonances, especially those with broad widths, remains a significant challenge. Traditional techniques such as the complex scaling method are often limited by sign problems or inherent statistical uncertainties. In this work, we present the first direct extraction of a nuclear resonance width within NLEFT by combining a high-precision, sign-problem-free nuclear interaction with the analytical continuation in the coupling constant (ACCC) approach. To address numerical instabilities in the ACCC framework, we implement a robust Pade solver based on singular value decomposition (SVD), incorporating ridge regularization and pole-safety criteria to ensure reliable extrapolation to the resonance pole. We detail the methodology and apply it to the unbound ground state of $^5$He ($J^π=3/2^-$). Our calculation yields a resonance energy $E=0.80(10)$ MeV and a width $Γ=1.05(9)$ MeV, in agreement with recent experimental results ($E_{\rm exp}=0.798$ MeV, $Γ_{\rm exp}=0.648$ MeV). This work establishes a practical and precise strategy for studying resonances within the ab initio lattice framework, paving the way for investigations of many-body resonances in exotic nuclei near the drip lines.

nucl-th↗

arXiv2026

Charge-dependent nucleon-nucleon interaction at N$^3$LO in nuclear lattice effective field theory

The nuclear lattice effective field theory (NLEFT) is an efficient tool for solving nuclear many-body problems, which takes high-fidelity lattice chiral interactions as input and computes nuclear low-energy observables via quantum Monte Carlo techniques. In this work, we present the first next-to-next-to-next-to-leading order (N$^3$LO) chiral forces on the lattice with the isospin-breaking effects fully taken into account. We focus on both the charge-independence breaking (CIB) and charge-symmetry breaking (CSB) effects. Specifically, we include the isospin-breaking effect from the mass difference between the charged and neutral pions in the one-pion-exchange potential (OPEP), the Coulomb force for the $pp$ interaction and the contribution of two additional charge-dependent contact operators. We also explicitly incorporate the two-pion-exchange potentials which was mostly neglected in previous NLEFT calculations. With these improvements, we are able to accurately reproduce the $np$ and $pp$ scattering phase shifts up to relative momentum $p \sim 200$ MeV as well as the deuteron properties. The construction of these charge-dependent lattice nuclear forces establishes a solid foundation for future high-precision nuclear ab initio calculations within the NLEFT framework.

nucl-th↗

arXiv2026

Investigating nuclear beta decay using lattice quantum Monte Carlo approach

We present an \textit{ab initio} calculation of nuclear $β$ decay within the framework of nuclear lattice effective field theory (NLEFT), employing auxiliary-field quantum Monte Carlo methods to solve the nuclear many-body problem. Our approach combines next-to-next-to-leading order two- and three-body chiral interactions with one- and two-body axial current operators, all consistently derived in chiral effective field theory. Low-energy constants are determined exclusively from nucleon-nucleon scattering phase shifts and few-body observables for systems with $A \leq 3$. Using these interactions and transition operators, we perform two-channel Monte Carlo simulations to compute the $β$-decay matrix element for $^6$He, obtaining results in reasonable agreement with experimental measurements. To address the Monte Carlo sign problem, we implement a perturbative expansion around a leading-order Hamiltonian with approximate Wigner-SU(4) symmetry. This systematic approach provides a foundation for extending NLEFT simulations to precision studies of weak processes in medium-mass nuclei.

nucl-th↗

arXiv2026

Sign-Problem-Free Nuclear Quantum Monte Carlo Simulation

Quantum Monte Carlo (QMC) methods offer exact solutions for quantum many-body systems but face severe limitations in fermionic systems like atomic nuclei due to the sign problem. While sign-problem-free QMC algorithms exist and provide valuable insights across disciplines, they have been restricted to simple models with limited quantitative predictive power. Here we overcome this barrier by developing a novel lattice nuclear force that is rigorously sign-problem-free for even-even nuclei. This interaction achieves a standard deviation of $σ= 2.932$ MeV from experimental binding energies for 76 even-even nuclei ($N,Z \leq 28$), matching state-of-the-art phenomenological mean-field models. Key innovations include the first sign-problem-free implementation of spin-orbit coupling for shell evolutions and an efficient QMC-optimized framework for global parameter fitting. Using this approach, we compute binding energies from $^4$He to $^{132}$Sn with unprecedented one-thousandth level numerical precision, reproduce symmetric nuclear matter saturation, and reveal novel spin-orbit-driven clustering in light nuclei. This work transforms sign-problem-free QMC into a scalable and predictive nuclear structure tool, while establishing a high-fidelity, non-perturbative foundation for \textit{ab initio} calculations of heavy nuclei.

nucl-th↗

arXiv2025

Impacts of isolated nucleon-nucleon correlations in relativistic $^{16}$O+$^{16}$O collisions

Nucleon-nucleon interactions are fundamental to the nuclear forces operating within the nucleus and play a crucial role in shaping the initial conditions of relativistic ion collisions through two-nucleon correlations. In this paper, we introduce an innovative approach to explore these encoded nucleon-nucleon correlations within advanced \textit{ab-initio} models in the context of relativistic $^{16}O$ collisions. Our methodology successfully reproduces the structural properties of the nucleonic configurations generated by these models, as well as the distance correlations between the nucleon pairs, denoted as $C(Δr)$. By generating nucleon positions that align with authentic configurations and adhering to the constraints imposed by the probability distribution of relative two-nucleon distances, our goal is to better understand nucleon-nucleon interactions within \textit{ab-initio} frameworks.

nucl-th↗

arXiv2025

Machine learning the single-$Λ$ hypernuclei with neural-network quantum states

Single-$Λ$ hypernuclei are the most straightforward extension of atomic nuclei. A thorough description of baryonic system beyond first-generation quark sector is indispensable for the maturation of nuclear $ab$ $initio$ methods. This study pioneers the application of neural-network quantum states to hypernuclei, with trainable parameters determined by variational Monte Carlo approach (VMC-NQS). In order to reduce the numerical uncertainty and treat the nucleons and hyperons in a unified manner, spinor grouping (SG) method is proposed to analytically integrate out isospin degrees of freedom. A novel spin purification scheme is developed to address the severe spin contamination occurring in standard energy minimization due to the weakly bound characteristic of light single-$Λ$ hypernuclei. The energy spectrum of $s$-shell hypernuclei is computed with one-thousandth level accuracy and benchmarked against existing stochastic variational results, showing superior performance. By comparing two different sets of Hamiltonian based on pionless effective field theory (pionless EFT), we choose an optimal model and further carry out calculations of selected $p$-shell charge-symmetric hypernuclei with mass number up to 13, exhibiting satisfactory consistency with experimental results. Our findings underscore the potential of VMC-NQS family in approaching exact solution of few-body systems and the accuracy of pionless EFT in modeling hypernuclei. This is crucial for understanding hyperon-nucleon-nucleon and hyperon-hyperon-nucleon interactions, providing a powerful tool for precisely predicting the properties of multi-strangeness hypernuclei.

nucl-th↗

arXiv2025

Machine Learning Unveils the Power Law of Finite-Volume Energy Shifts

Finite-volume extrapolation is an important step for extracting physical observables from lattice calculations. However, it is a significant challenge for the system with long-range interactions. We employ symbolic regression to regress finite-volume extrapolation formula for both short-range and long-range interactions. The regressed formula still holds the exponential form with a factor $L^n$ in front of it. The power decreases with the decreasing range of the force. When the range of the force becomes sufficiently small, the power converges to $-1$, recovering the short-range formula as expected. Our work represents a significant advancement in leveraging machine learning to probe uncharted territories within particle physics.

hep-ph↗

arXiv2025

Super-bath Quantum Eigensolver

The simulation of the dynamics of a system coupled to a low-temperature environment is a promising application of quantum computers to determine ground-state properties of physical systems. However, this approach requires not only the $\textit{existence}$ of an environment that allows the system to dissipate energy and evolve to its ground state, but also the $\textit{detailed knowledge}$ of the properties of the bath. In this paper, we propose a polynomial-time algorithm for ground state preparation which only relies on the $\textit{existence}$ of a physical bath which achieves the same task, while a detailed description of the environment may remain $\textit{unknown}$. In particular, we show that this ``super-bath quantum eigensolver algorithm'' prepares the ground state of the system by combining a Gaussian stabilization dephasing procedure with the simulation of the interaction between the system and a super-bath which only requires minimal knowledge of the physical environment. Based on our algorithmic framework, we establish a partial order relation among environments. Supported by experimental lifetime data of nuclear metastable states, we suggest that our algorithm is applicable to determine nuclear ground states in polynomial time. These results highlight the potential advantage of quantum computing in addressing ground state problems in real-world physical systems.

quant-ph↗