This work presents the first lattice calculation of a two-to-two particle matrix element of a local current. This exploratory calculation is performed using a leading-order pionless effective field theory of two nucleons in a finite 3D spatial volume, where the Hamiltonian can be diagonalized exactly for moderate volumes. By considering a range of couplings where the theory supports a deuteron-like bound state, we determine the finite-volume spectra and matrix elements of the conserved local vector current. Using the Lüscher formalism, we constrain the infinite-volume, purely hadronic amplitude for this theory. Using previously derived formalism, we then map the finite-volume matrix elements to scattering amplitudes describing a reaction coupling two-particle states via a current insertion, $\2+\Jc \to \2$. We then use a recently derived relation between this class of amplitudes and the bound-state elastic form factor to directly constrain the infinite-volume form factor. By varying over a range of values of the coupling of the theory, we explore the effects of this analysis for deep-bound states and shallow-bound states. We reproduce the expected result that for deep bound states, the finite-volume formalism is largely unnecessary, while for shallow bound states, it is absolutely critical to obtain a sensible result. We present a detailed outline of the analysis of this class of matrix elements, including the determination of the charge radius of the bound state. In the shallow bound state limit, we find good agreement with the prediction stemming from the anomalous threshold.

We enable the automatic construction of Hybrid Monte Carlo (HMC) forces in lattice gauge theory by performing reverse-mode automatic differentiation at the level of optimized LLVM intermediate representation, making the approach applicable to any language that lowers lattice action code to LLVM. In practice, this means that once the action evaluation routine is implemented, the corresponding HMC force can be generated automatically from the same code path, without deriving or maintaining a separate force routine. The method preserves conventional imperative, in-place implementations and enables a single-source workflow in which forces are generated directly from the action code while inheriting compiler optimizations. We perform end-to-end reverse-mode differentiation of both gauge and Wilson fermion actions. For the Wilson fermion case, we find that the force generated by automatic differentiation achieves performance comparable to a conventional hand-written fermion force implementation. The same differentiation pipeline targets both CPU and GPU backends, providing a practical route to performance-portable force construction for compositional lattice actions.

The doubly charmed tetraquark $T_{cc}(3875)^+$ observed at LHCb has attracted considerable interest in recent years. To accurately determine its finite-volume spectrum, a variational analysis using a large basis of operators, including bilocal scattering operators, but also local tetraquark operators, should be employed. Using Wilson-clover fermions at the $SU(3)$-flavour-symmetric point, we investigated the importance of local tetraquark operators for the $T_{cc}$ spectrum by adding them to a large basis of bilocal $DD^*$ and $D^*D^*$ scattering operators. We performed this calculation using the distillation framework combined with a position-space sampling method that we recently developed. This method makes local tetraquark operators affordable in distillation. Upon including local tetraquark operators, we observe significant shifts in the estimates of several energy levels. Finally, we show the effect of these shifts on the $DD^*$ scattering phase shifts obtained from a single-channel $s$-wave Lüscher analysis.

In this work we investigate the influence of weak acceleration on the confinement-deconfinement phase transition in gluodynamics. Our study is carried out within lattice simulation in the comoving reference frame of accelerated observer which is parameterized by the Rindler coordinates. We find that finite temperature confinement-deconfinement phase transition turns into spatial crossover in the Rindler spacetime. In other words, spatially separated confinement and deconfinement phases can coexist in the Rindler spacetime within certain intervals of temperature and acceleration. We determine the position of the boundary between the phases as a function of temperature for several accelerations and find that it can be described by the Tolman-Ehrenfest law with rather good accuracy although a minor deviation takes place. Moreover, the critical temperature of the system in the weak acceleration regime is found to remain unchanged as that of the standard homogeneous gluodynamics. Our results imply that the spatial confinement-deconfinement transition might take place in the vicinity of the Schwarzschild black hole horizon.

Hamiltonian formulations of lattice field theories provide access to real-time dynamics, but their simulation is difficult to implement efficiently. Trotter-Suzuki decompositions are at the center of time evolution computation, either on quantum hardware or classically, for instance with the use of tensor networks. While low-order Trotterizations remain the standard choice due to their simplicity, higher-order schemes offer the potential for improved efficiency. In this work we outline a short guide to Trotter-Suzuki schemes and their implementations in general. To help with this, we highlight new efficient schemes found by our optimization framework, and demonstrate their performance on the Heisenberg model.

We present charmonium spectral functions extracted from Euclidean-time correlation functions using sparse modeling (SpM). SpM solves inverse problems by considering only the sparsity of the target solution. To assess the applicability of the method, we first test it with mock data designed to mimic charmonium correlation functions. We demonstrate that while resonance peaks in the spectral functions can be reconstructed using this method, transport peaks are difficult to resolve without introducing further assumptions beyond sparsity. We then apply the method to charmonium correlation functions obtained from lattice QCD at temperatures below and above the critical temperature. The results are found to be qualitatively consistent with those obtained using the maximum entropy method, although the transport peak is not clearly resolved. This indicates that, even when relying solely on the assumption of sparsity, the method can capture some relevant features of the underlying physics.