We present a first study of a diffusion-based approach to accelerated sampling of the $N_f = 2$ lattice Schwinger model. Our work is inspired by recent and growing successes in developing such generative models for ensemble generation in LFT to overcome the well-known critical slowing down problem. We train a U(1)-equivariant score-based generative model to sample gauge link configurations from the marginal Schwinger model. By computing model likelihoods, we obtain unbiased estimates for observables that closely match those produced by MCMC simulations. We also demonstrate improvement over HMC as measured qualitatively by a reduction in topological freezing near critical parameters.

We propose a formulation of the overlap Dirac operator in lattice QCD that employs diagonal Kenney-Laub (KL) iterates to approximate the matrix sign function. KL iterates require no prior spectral information about the kernel operator and, when expressed via their partial fraction decomposition, offer a practical and efficient approximation scheme. We evaluate this approach in a proof-of-concept implementation using quenched lattices at $\beta=6.2$ and two Dirac operator discretizations as a kernel, namely the Wilson and the Brillouin operators. By examining the approximate overlap operator's violation of the Ginsparg-Wilson relation and the critical bare quark mass for increasing approximation order, we find that KL iterates deliver enhanced chiral symmetry preservation and computational efficiency compared to the Chebyshev polynomial approach.

We construct the traceless components of the energy-momentum tensor on the lattice for QCD with $N_f=3$ flavours, such that their correlation functions satisfy the appropriate Ward identities in the continuum limit. To carry out this program, we define the theory on the lattice by the Wilson-plaquette and the $O(a)$-improved Wilson actions for gluons and quarks respectively. The discretization of the space-time entails that (i) the irreducible nonet representation of the SO($4$) group splits into a triplet and a sextet irreducible representations of the hypercubic group, and (ii) for each multiplet non-perturbative determinations of the the gluonic and fermionic renormalization constants are required. The bare gluonic components of the energy-momentum tensor are defined via the clover discretization of the field strength tensor, while the fermionic ones are discretized by appropriate combinations of symmetric covariant derivatives. Either for the triplet or the sextet representations, the two independent renormalization constants are then fixed non-perturbatively by imposing discretized versions of continuum Ward identities for one-point correlation functions in the presence of shifted boundary conditions and an imaginary chemical potential. The non-perturbative calculation is then carried out by Monte Carlo simulations, and the resulting renormalization constants are determined with a final accuracy of a few percent for values of the bare coupling constant squared in the range $0 \leq g_0^2\leq 0.96$.

We investigate the phase transition of Quantum Chromodynamics (QCD) with three degenerate quark flavors at zero baryon chemical potential. Using Möbius domain-wall fermions as the lattice fermion formulation, we ensure excellent chiral symmetry preservation. Our simulations are performed at three different temporal lattice extents, $N_{t}=6, 8, 12$, with a fixed lattice spacing $a=0.1361(20)$ fm, corresponding to temperatures of 242(4), 181(3), and 121(2) MeV, respectively. We explore a range of quark masses and spatial volumes with aspect ratios $N_{s}/N_{t}$ spanning from 2 to 4. By analyzing the mass and volume dependencies of the plaquette, plaquette susceptibility, chiral condensate, chiral susceptibilities, and Binder cumulant, we identify the pseudocritical transition quark masses from our largest lattice volumes. For $N_t=6$, this is 184(10) MeV (determined from the plaquette susceptibility). For $N_t=8$ and 12, the transition points vary slightly depending on whether the total or disconnected chiral susceptibility is used, yielding ranges of 36(1)-39.1(9) MeV and 3.5(3)-3.7(2) MeV, respectively, in the $\overline{\text{MS}}$ scheme at a scale of $\mu=2$ GeV. The negligible volume dependence at $N_t=6$ and 8, combined with finite-size scaling analysis at $N_t=12$ revealing volume growth significantly weaker than expected for a first- or second-order phase transition, points to a continuous crossover at these specific quark mass points. Additionally, we study the effects of residual chiral symmetry breaking on the chiral condensate and chiral susceptibilities using two different values of $L_s$.

We present a first-principles lattice-QCD determination of Mellin moments of the unpolarized pion and kaon parton distribution functions using matrix elements of boosted mesons coupled to nonlocal operators containing a straight Wilson line. The calculation is performed on an $N_f=2+1+1$ ensemble of maximally twisted-mass fermions with a clover term, with lattice volume $32^3\times64$, lattice spacing $a=0.0934$ fm, and pion mass $m_\pi=260$ MeV. Matrix elements are computed for hadron momenta $P_3=0$, 0.41, 0.83, 1.25, 1.66, and 2.07 GeV and analyzed within the short-distance factorization framework. We investigate the dependence of the extracted moments on the truncation of the operator-product expansion, the coordinate-space fit window, and the perturbative accuracy of the Wilson coefficients, comparing next-to-leading-order and next-to-next-to-leading-order results. We also perform an RG-improved analysis as a consistency check of the perturbative treatment. Our final results are obtained from combined fits in $(P_3,z)$ space at next-to-next-to-leading-order and are quoted at $\mu=2$ GeV. We also study the SU(3) symmetry-breaking effect and reconstruct the valence PDFs from the moments.

Spectral densities link experimental measurements to dynamical properties of a quantum field theory which, in turn, can be resolved non-perturbatively from the Euclidean time-dependence of correlation functions. By making extensive use of integral transforms, we present analytic formulae to carry out the inverse Laplace transform so as to extract spectral densities from either the continuum or the discrete sampling of correlation functions in the Euclidean time. Formulae extend to regulated and/or smeared spectral densities as well. We explicitly show that the proposed lattice solution tends to its continuum counterpart up to $O(a^2)$ effects in the lattice spacing $a$ if the lattice correlator is $O(a)$-improved. In practical computations, lattices have necessarily a finite Euclidean temporal extent, a lack of knowledge which suggests to introduce incomplete integral transforms and the corresponding incomplete smeared spectral densities. The contribution from the unknowns to a smeared spectral density can then be rigorously bound and kept under control if the integral transform of the smearing function decays fast enough with the conjugate variable. Conversely, the bound can be used to plan lattices so as to achieve a given target precision on the reconstructed spectral density of interest. The formulae presented here in the context of lattice field theory can be easily applied or extended to other areas of research.

We present a comprehensive review of regularization schemes for magnetized dense quark matter within effective models of quantum chromodynamics, focusing on the Magnetic-Field-Independent Regularization (MFIR) and the Medium Separation Scheme (MSS) at finite chemical potential and magnetic field. In nonrenormalizable frameworks such as the Nambu-Jona-Lasinio model, the treatment of ultraviolet divergences is crucial, particularly in magnetized and dense environments where conventional regularization procedures may introduce unphysical artifacts. We show that MFIR consistently isolates divergent vacuum contributions from finite magnetic-field-dependent terms, while MSS extends this separation to the medium sector, ensuring that only vacuum quantities are regularized. Within this unified framework, we analyze the thermodynamics of cold and dense quark matter, including color-superconducting phases, and demonstrate that the superconducting gap remains finite at large chemical potentials, even in the presence of strong magnetic fields. In contrast to results obtained with traditional regularization schemes, we find no evidence for a transition to a normal phase at zero temperature, highlighting the importance of a proper separation between vacuum and medium contributions. These results eliminate spurious oscillations and other nonphysical artifacts, leading to a more robust and physically consistent description of strongly interacting matter under extreme conditions relevant to compact stars and heavy-ion collisions.

We investigate the configurational temperature estimator in interacting matrix models and Gaussian random-matrix ensembles. The estimator follows from an exact Schwinger--Dyson identity and may be expressed in terms of the gradient and Hessian of the action. We study the Gross--Witten--Wadia model, a quartic double-well matrix model, and the Gaussian Orthogonal, Unitary, and Symplectic Ensembles. In all cases, the estimator satisfies the exact Schwinger--Dyson identity, $\beta_{\rm config} = 1$, within statistical uncertainties. Separating the estimator into isotropic and anisotropic parts, we find that the leading finite-$N$ corrections satisfy the approximate relation $\beta_{\rm iso} - 1 \simeq - \beta_{\rm aniso}$. We also show that the configurational temperature estimator provides a sensitive diagnostic of Monte Carlo simulations.

We investigate the analytic structure of the quark propagator in the Landau gauge by dynamically coupling the standard gap equation to the non-perturbative quark-gluon vertex. Employing the full vertex basis, we demonstrate that for sub-GeV time-like momenta, the proper inclusion of the underlying dynamics leads to a pair of real poles with opposite-sign residues. In particular, in stark contradistinction to the results obtained in widely used approximations, we see no sign of complex conjugate poles. This distinctive analytic structure evades conceptual shortcomings frequently associated with complex conjugate poles while remaining fully compatible with the aspects of color confinement related to positivity violation. Crucially, this novel behavior is governed by a dominant triplet of vertex form factors: the tree-level component, the anomalous chromomagnetic moment, and a component we label as "spin-momentum curvature". By gradually tuning the individual strengths of these components, we demonstrate that while they contribute in distinct ways to the quark propagator, their joint action is vital for stabilizing the system. Together, they place the low-lying poles onto the real axis while producing a robust constituent quark mass of $350$ MeV.