Excited-state contamination remains one of the leading sources of systematic uncertainty in the precise determination of hadron structure observables from lattice QCD. In this work, I present a general mechanism, motivated by meson dominance and implemented through the variational method, that identifies which excited states are enhanced by the choice of inserted current and kinematics. The argument is supported by numerical evidence and predictions from chiral perturbation theory across different hadronic channels, in particular in the nucleon sector, and provides both conceptual insight and practical guidance for controlling excited-state effects in hadron three-point function analyses.

We discuss an ongoing first lattice study of the doubly-charmed tetraquark $T_{cc}^+$(3875) via a three-body approach. We investigate the $DD\pi$ system in the $I=0$, $C=2$ sector, where the $T_{cc}^+$ appears as a pole in the $J^P = 1^+$ $DD\pi$ elastic scattering amplitude. The approach automatically incorporates two-body $DD^*$ and three-body $DD\pi$ effects and treats left-hand cuts due to single $\pi$ exchanges. Two CLS ensembles, X252 and X253, with pion mass $M_\pi \approx 280$ MeV, are used, and an operator set comprised of two- and three-hadron and tetraquark operators is employed to extract finite-volume energies. Additional inputs are required for the three-body finite-volume analysis, in the form of amplitudes for the $I=1$ $DD$ and $I=1/2$ $D\pi$ two-body subsystems. We present preliminary results for these subchannels and perform exploratory three-body spectra determinations for simple choices of the three-particle K-matrix $\mathcal{K}_{\text{df}, 3}$, allowing a first comparison to the lattice spectrum.

We study how the isospin asymmetry affects quarkonium states in QCD at near zero temperature. Using lattice Non-Relativistic QCD formalism, we calculate bottom quark correlators in the gauge field ensembles generated with $N_f = 2 + 1$ flavors of dynamical staggered quarks whose dynamics include the isospin chemical potential effect and then construct $S-$ and $P-$ wave quarkonium state correlators. From these quarkonium correlators, we consider the ratios of quarkonium correlators at non-zero isospin chemical potential to that at $\mu_I a = 0.000$. Here, the gauge field ensemble with $\mu_I a = 0.000, 0.048, 0.053, 0.059, 0.066, 0.080, 0.092$ and $0.106$ on a $32^3 \times 48$ lattice with non-zero isospin current strength $\lambda a = 0.0010, 0.0018,$ and $0.0036$, where $m_\pi = 135$ MeV and $a = 0.1535$ fm from \cite{Brandt:2022hwy}, are used. Preliminary results suggest that for $\mu_I a = 0.106$, the Upsilon mass gets heavier than the Upsilon mass in the vacuum and that below $\mu_I a = 0.106$ the isospin asymmetry effect on the Upsilon mass is not monotonic.

The kaon, the lightest hadron containing a strangeness quark, is very peculiar. It is a Nambu-Goldstone boson, but significantly heavier than the pion. As a result, its interaction with a matter particle, such as the nucleon or a heavy-light meson, such as the $D$ meson, is completely determined by chiral dynamics and much stronger than its pion cousin. The strong attractive interaction has brought us many surprises and is manifested in the peculiar nature of many particles, such as the mysterious $\Lambda(1405)$ and $D_{s0}^*(2317)$. These two particles can be understood as $\bar{K}N$ and $DK$ hadronic molecules, respectively. They also imply the existence of three-body hadronic molecules that await future discovery. In this talk, I review some recent developments in our understanding of hadronic interactions involving the kaon.

We present a detailed account of the theoretical progress and the computational strategy that led to the non-perturbative determination of the QCD Equation of State at temperatures up to the electroweak scale reported in [Phys. Rev. Lett. 134, 201904 (2025)]. The two key ingredients that make such a calculation feasible with controlled uncertainties are: (i) the definition of lines of constant physics through the running of a non-perturbatively defined finite-volume coupling across a wide range of energy scales, and (ii) the use of shifted boundary conditions which allow a direct determination of the entropy density thus without the need for a zero-temperature subtraction. Considering the case of QCD with $N_f =3$ massless flavours in the temperature interval between 3 GeV and 165 GeV, we describe the numerical strategy based on integrating in the bare coupling and quark mass, the perturbative improvement of lattice observables, the optimization of numerical simulations, and the continuum extrapolation. Extensive consistency checks, including finite-volume and topological-freezing effects, confirm the robustness of the method. The final results have a relative accuracy of about $1\%$ or better, and the errors are dominated by the statistical fluctuations of the Monte Carlo ensembles. We also compare our non-perturbative results with predictions from standard and hard thermal loop perturbation theory showing that at the level of $\%$-precision contributions beyond those known, including non-perturbative ones due to ultrasoft modes, are relevant up to the highest temperatures explored. The methodological framework is general and readily applicable to QCD with four and five massive quark flavours and to other thermal observables, paving the way for systematic non-perturbative studies of thermal QCD at very high temperatures.

For the first time, we implement the deep-neural-network-based variational Monte Carlo approach for the multiquark bound states, whose complexity surpasses that of electron or nucleon systems due to strong SU(3) color interactions. We design a novel and high-efficiency architecture, DeepQuark, to address the unique challenges in multiquark systems such as stronger correlations, extra discrete quantum numbers, and intractable confinement interaction. Our method demonstrates competitive performance with state-of-the-art approaches, including diffusion Monte Carlo and Gaussian expansion method, in the nucleon, doubly heavy tetraquark, and fully heavy tetraquark systems. Notably, it outperforms existing calculations for pentaquarks, exemplified by the triply heavy pentaquark. For the nucleon, we successfully incorporate three-body flux-tube confinement interactions without additional computational costs. In tetraquark systems, we consistently describe hadronic molecule $T_{cc}$ and compact tetraquark $T_{bb}$ with an unbiased form of wave function ansatz. In the pentaquark sector, we obtain weakly bound $\bar D^*\Xi_{cc}^*$ molecule $P_{cc\bar c}(5715)$ with $S=\frac{5}{2}$ and its bottom partner $P_{bb\bar b}(15569)$. They can be viewed as the analogs of the molecular $T_{cc}$. We recommend experimental search of $P_{cc\bar c}(5715)$ in the D-wave $J/\psi \Lambda_c$ channel. DeepQuark holds great promise for extension to larger multiquark systems, overcoming the computational barriers in conventional methods. It also serves as a powerful framework for exploring confining mechanism beyond two-body interactions in multiquark states, which may offer valuable insights into nonperturbative QCD and general many-body physics.

In high-energy physics, confinement denotes the tendency of fundamental particles to remain bound together, preventing their observation as free, isolated entities. Interestingly, analogous confinement behavior emerges in certain condensed matter systems, for instance, in the Ising model with both transverse and longitudinal fields, where domain walls become confined into meson-like bound states as a result of a longitudinal field-induced linear potential. In this work, we employ the Ising model to demonstrate that Krylov state complexity--a measure quantifying the spread of quantum information under the repeated action of the Hamiltonian on a quantum state--serves as a sensitive and quantitative probe of confinement. We show that confinement manifests as a pronounced suppression of Krylov complexity growth following quenches within the ferromagnetic phase in the presence of a longitudinal field, reflecting slow correlation dynamics. In contrast, while quenches within the paramagnetic phase exhibit enhanced complexity with increasing longitudinal field, reflecting the absence of confinement, those crossing the critical point to the ferromagnetic phase reveal a distinct regime characterized by orders-of-magnitude larger complexity and display trends of weak confinement. Notably, in the confining regime, the complexity oscillates at frequencies corresponding to the meson masses, with its power-spectrum peaks closely matching the semiclassical predictions.