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In the study of strongly interacting quantum systems, a remarkable feature is the emergence of universal behavior that is independent of the underlying microscopic interactions. This type of universality happens when the two-body scattering length is much larger than the range of the interaction~\cite{Braaten2006,Naidon2017}, with examples ranging from quantum chromodynamics (QCD) to atomic physics~\cite{Hammer2010,Chin2010,Hammer2013}. In this regime, the details of the short-range forces are largely irrelevant, and low-energy properties are dictated by only a few parameters.

The helium dimer corresponds to one of the best examples of a naturally occurring physical system displaying this universality~\cite{Nielsen1998}. Its exceptionally weak binding energy and large scattering length provide one of the cleanest setups to explore universality, paralleling phenomena observed in nuclear systems such as the deuteron and halo nuclei.

A central element in computing properties of helium systems is the construction of interatomic potentials that capture the He-He interaction. The helium dimer is extremely weakly bound, with a binding energy on the order of 1 mK and a bond length of approximately 50 \AA. Such a delicate system amplifies the sensitivity to the details of the underlying potential, and small variations in the short-range repulsion or the long-range van der Waals attraction can lead to significant changes in its properties.

For this reason, a sequence of increasingly sophisticated He-He potentials has been developed, ranging from early empirical Lennard-Jones forms~\cite{Jones1924,Jones1925,Boer1938,Aziz1979} to combinations of phenomenological input and ab initio models to produce accurate potentials, such as HFDHE2~\cite{Aziz1979}, LM2M2~\cite{Aziz1991}, and the SAPT~\cite{Korona1997,Janzen1997} series. These potentials are designed to reproduce experimental data while remaining consistent with the known dispersion forces that dominate at large separations.

This variety of He-He potentials has enabled testing the concept of universality among them: although their short-range structures differ, they yield remarkably consistent predictions for low-energy observables. This convergence illustrates that universality is not an artifact of any specific potential, but rather a genuine feature of helium systems close to the unitary regime.

At this point, a question arises: what is the minimal information that must be encoded in an interaction to reproduce the universal behavior? The SAPT potential family, which provides an excellent description of the $^4$He dimer, has 40 parameters~\cite{Korona1997,Janzen1997}. We must be able to capture the universal aspects of the helium-4 dimer with a more simplified description than that.

The answer, at least for two-body systems, is readily available using low-energy scattering theory~\cite{Newton2013,kievsky2021,Lima2023,Madeira2024}. The usual textbook assumptions are that the potential is real, finite-ranged, local, and spherically-symmetric, which may seem too restrictive at first glance but, in fact, apply to several physical systems. The effective range expansion (ERE)~\cite{Bethe1949} shows that the $s$-wave scattering length $a$ and effective range $r_0$ are related to the low-energy phase shift $\delta_0(k)$ through:
\begin{equation}
k \cot \delta_0(k) = -\frac{1}{a}+\frac{r_0 k^2}{2} + \mathcal{O}(k^4).
\end{equation}
Analyzing the poles of the S-matrix and employing the ERE, it is possible to obtain approximations for the dimer binding energy $E_2$ (or the energy of the virtual states in case of $a<0$) within low-energy scattering theory~\cite{Newton2013,kievsky2021,Lima2023,Madeira2024},
\begin{equation}
E_{\rm zr}=-\frac{\hbar^2}{2 m_r a^2} \ \text{ (zero range)\, and} \,\,
E_{\rm fr}=-\frac{\hbar^2}{2m_r r_0^2}\left(1-\sqrt{1-\frac{2 r_0}a}\right)^2 \text{(finite range)},
\end{equation}
where $m_r$ is the reduced mass. For the helium dimer computed with realistic potentials, typically $E_{zr}/E_2\sim 0.9$ and $E_{fr}/E_2\sim 1$, meaning that the scattering length alone provides a simple description that captures most of the physics, while including range corrections provides excellent agreement between low-energy scattering theory and the physical system. The $^4$He dimer is an excellent example of this low-energy universality, which is not restricted to atomic physics and has numerous applications in both atomic and nuclear physics~\cite{kievsky2021}.

The rich physics presented by the helium dimer is further augmented when we consider the trimer. Since this system corresponds to three identical bosons with large scattering lengths, the Efimov effect plays an important role in its description~\cite{Efimov1970,Efimov1971}. Although Efimov physics is naturally occurring in this system, in opposition to engineered Feshbach resonances in cold atom systems, its experimental observation was very challenging~\cite{Kunitski2015}. As a matter of fact, all experimental investigations concerning $^4$He few-body clusters are very challenging~\cite{Grisenti2000,Voigtsberger2014,Kunitski2015,Zeller2016}.
An alternative to investigate these systems is to perform ``numerical experiments'', where a realistic potential is chosen to compute properties of $^4$He clusters and matter~\cite{Kalos1981,Pandharipande1983,Kievsky2011}.

An alternative description of strongly interacting systems, such as atomic helium-4, can be achieved through Effective Field Theories (EFTs). They have been successful in describing systems in nuclear physics~\cite{Kolck1999,Bedaque2002,Hammer2020,vanKolck2020}, including the promising scheme of developing it as an expansion around unitarity~\cite{Konig2017}, and atomic physics~\cite{Bazak2016,Bazak2019}.

Systems comprised of atomic $^4$He, clusters and bulk matter, provide an excellent setting for developing EFTs for strongly interacting systems. Nucleon systems correspond to four-component fermions, and the nuclear interaction is spin-isospin dependent, in addition to including non-central interactions and higher-order derivatives. On the other hand, $^4$He atoms present bosonic statistics and, in the energy regime we are interested in here, interact via short-range spherically symmetric potentials. Hence, these systems present an opportunity to study and develop EFTs in a much simpler setting, while retaining the physics of strongly interacting systems. The expectation is that what is learned in these systems can be used to improve EFTs in the nuclear sector.

The progress on developing EFTs for $^4$He shows promise. For $N\leqslant 6$ clusters, leading-order (LO) and next-to-leading-order (NLO) results~\cite{Bazak2019} suggest that it is possible to describe these systems in a systematically improvable expansion. Additionally, they show that a four-body force emerges perturbatively at NLO and that no additional three-body counterterm is required beyond LO.

The next step in the EFT program should be to tackle many-body systems: $N\geqslant 7$ clusters and matter. In this direction, the Quantum Monte Carlo (QMC) results presented in Ref.~\cite{Carlson2017} are encouraging. They present results for $N\leqslant 60$ clusters and matter consisting of unitary bosons. One of the main findings is that for sufficiently loosely bound trimers, the properties of these many-body systems are universal. Although the helium-4 dimer is not at unitarity, its scattering length is large compared to the effective range, hence an EFT describing many-body systems of $^4$He seems within reach.

The workshop sparked several discussions on how to improve ab initio many-body calculations of strongly interacting systems within the EFT framework. In the following, I will present some of the points raised, along with possible explorations to address them. One that received much attention is concerning the cutoff employed in the calculations. Ideally, we want to be able to push the cutoff much larger than the typical momentum scales of the system under study, but numerically this can be very challenging. In two-component Fermi gases, where the Pauli exclusion principle suppresses a three-body scale, QMC simulations in strongly interacting regimes have been performed with zero-range interactions~\cite{Pessoa2019}. Although the proposed scheme would work only for two-body interactions, it is still worth considering implementing it in bosonic simulations. The three-body force would still have a finite cutoff in the simulations, but treating the two-body interactions exactly at zero range could in principle make observables converge faster with the cutoff.

Another possibility to enhance EFTs is what is known as an improved action~\cite{Contessi2024,Contessi2024b}. An improved action is a modified version of an EFT action in which higher-order operators are added with tuned coefficients to systematically reduce errors at finite cutoffs. This must be done carefully and consistently, so that these promotions can be compensated perturbatively at higher orders. For example, the effective range cannot be promoted to LO, otherwise it would violate the Wigner bound~\cite{Wigner1955}, but a fraction of it can. Exploring the choices of improved actions and their impact on many-body systems, as well as the convergence of EFTs, is another important and promising direction for the field.

Quantum Monte Carlo calculations are ab initio, nonperturbative many-body approaches capable of accurately describing strongly interacting systems by directly solving the Schr\"odinger equation using stochastic sampling of the many-body wave function without relying on mean-field or perturbative approximations. In particular, Diffusion Monte Carlo (DMC) is a stochastic projection method that evolves a trial wave function in imaginary time toward the ground state yielding, apart from controllable statistical uncertainty, exact results for bosonic systems, since their ground-state wave function is free from the fermionic sign problem. In DMC simulations, quantities associated with operators that do not commute with the Hamiltonian cannot be evaluated exactly, since the mixed estimator depends on the trial wave function, leading to a systematic bias that can only be mitigated through extrapolation or more advanced techniques. Besides being a problem for obtaining spatial and momentum distributions at LO, this limitation also affects NLO calculations directly, where matrix elements should be computed with the LO ground state wave function. Variational calculations do not suffer from this issue, but constructing accurate many-body wave functions for strongly interacting systems is a challenging task. Recently, neural-network-based wave functions have emerged as a promising solution, providing highly expressive and systematically improvable representations of many-body states that can capture complex correlations and thus improve both variational accuracy and the quality of trial wave functions used in QMC simulations~\cite{Lovato2022}.

A crucial aspect of modern EFT and ab initio approaches is uncertainty quantification, where statistical, systematic, and theoretical uncertainties are rigorously estimated and propagated to observables, often visualized through error bands that reflect the predictive reliability and convergence of the theory. A significant challenge in applying EFTs to strongly interacting systems is the computational cost of solving few- and many-body problems with high accuracy. This becomes particularly demanding when uncertainty quantification requires exploring large parameter spaces. Emulators provide an efficient solution: they are models trained on a limited set of full high-precision EFT calculations that can then rapidly predict observables at new parameter values~\cite{Furnstahl2015,Melendez2017,Melendez2019,Curry2025}. In particular, eigenvector continuation has emerged as a powerful method to emulate many-body calculations across parameter space~\cite{Frame2018}. By learning from a small set of full solutions, eigenvector continuation enables rapid and accurate predictions for large systems, making systematic uncertainty quantification feasible.

The discussions at the workshop highlighted how Effective Field Theory provides a unifying language for describing strongly interacting systems, from atomic helium to nuclear matter. The helium-4 system remains a particularly clean arena for testing ideas of universality and developing systematically improvable EFT formulations. Ongoing efforts to better control cutoff effects, design improved actions, and integrate modern tools such as neural-network wave functions and emulators are paving the way toward more accurate and efficient ab initio studies. Beyond helium, these developments promise to deepen the connection between atomic and nuclear physics, advancing our understanding of strongly correlated quantum systems in general, from few- to many-body.

\begin{acknowledgments}
We thank ECT* and INFN (Istituto Nazionale di Fisica Nucleare) for support in the framework of the ECT*/INFN Workshop ``Universality in strongly-interacting systems: from QCD to atoms'' during which this work has been initiated.
\end{acknowledgments}

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