We present a systematic lattice calculation of the vector and axial vector form factors $V$ and $A_i~(i=0,1,2)$ for the $D_s \to \phi \ell \nu_\ell$ semileptonic decay using (2+1)-flavor Wilson-clover fermion configurations generated by the CLQCD collaboration. Seven gauge ensembles with different lattice spacings, from $0.052~\text{fm}$ to $0.105~\text{fm}$, and different pion masses, from about $210~\text{MeV}$ to $320~\text{MeV}$ are utilized, enabling us to take both the continuum limit and physical pion mass extrapolation. The form factor ratios are obtained to be $r_V=1.614(19)$ and $r_2=0.741(31)$. Our results of form factors reach the precision of $1\%-4\%$, which greatly improves the previous lattice QCD results and obtains the most precise determination to date.

We study the color correlation between two static quarks in 3Q ($QQQ$) and 4Q ($QQ\bar Q\bar Q$) multiquark systems at $T=0$ based on the reduced two-body density matrices $\rho$ in color space. We perform quenched lattice QCD calculations with the Coulomb gauge adopting the standard Wilson gauge action, and the spatial volume is $L^3 = 32^3$ at $\beta = 5.8$, which corresponds to the lattice spacing $a=0.14$ fm and the system volume $L^3=4.5^3$ fm$^3$. We evaluate the two-body color density matrix $\rho$ of static quarks, and investigate the dependence of color correlations on the quarks' spatial configuration. As a result, we find that the color correlations depend on the minimal path length along a flux tube which connects two quarks under consideration. The color correlation between quarks quenches because of color leak into the gluon field (flux tube) and finally approaches the random color configuration in the large distance limit. We find a ``universality'' in the flux-tube path length dependence of the color leak for 2Q, 3Q, and 4Q ground-state systems.

We introduce a dynamical-lattice regulator (DLR) for Euclidean quantum field theories on a fixed hypercubic graph $\Lambda \simeq \mathbb{Z}^d$, in which the embedding $x:\Lambda \to \mathbb{R}^d$ is promoted to a dynamical field and integrated over subject to shape-regularity constraints. The total action is local on $\Lambda$, gauge invariant, and depends on $x$ only through Euclidean invariants built from edge vectors (local metrics, volumes, etc.), hence the partition function is exactly covariant under the global Euclidean group SE(d) at any lattice spacing. The intended symmetry-restoring mechanism is not rigid global zero modes but short-range *local twisting* of the embedding that mixes local orientations; accordingly, our universality discussion is conditioned on a short-range geometry hypothesis (SR): after quotienting the global SE(d) modes, connected correlators of local geometric observables have correlation length O(1) in lattice units. We prove Osterwalder-Schrader reflection positivity for the coupled system with embedding $x$ and generic gauge/matter fields $(U,\Phi)$ in finite volume by treating $x$ as an additional multiplet of scalar fields on $\Lambda$. Assuming (SR), integrating out $x$ at fixed cutoff yields a local Symanzik effective action in which geometry fluctuations generate only SO(d)-invariant irrelevant operators and finite renormalizations; in particular, in $d=4$ we recover the standard one-loop $\beta$-function in a scalar $\phi^4$ test theory. Finally, we describe a practical local Monte Carlo update and report $d=2$ proof-of-concept simulations showing a well-behaved geometry sector and a substantial reduction of axis-vs-diagonal cutoff artifacts relative to a fixed lattice at matched bare parameters.

While quantum simulators promise to explore quantum many-body physics beyond classical computation, their capabilities are limited by the available native interactions in the hardware. On many platforms, accessible Hamiltonians are largely restricted to one- and two-body interactions, limiting access to multi-body Hamiltonians and to systems governed by simultaneous, non-commuting interaction terms that are central to condensed matter, quantum chemistry, and high-energy physics. We introduce and experimentally demonstrate a hybrid digital-analog protocol that overcomes these limitations by embedding analog evolution between shallow entangling-gate layers. This method produces effective Hamiltonians with simultaneous non-commuting three- and four-body interactions that are generated non-perturbatively and without Trotter error -- capabilities not practically attainable on near-term hardware using purely digital or purely analog schemes. We implement our scheme on a trapped-ion quantum processor and use it to realize a topological spin chain exhibiting prethermal strong zero modes persisting at high temperature, as well as models featuring three- and four-body interactions. Our hardware-agnostic and scalable method opens new routes to realizing complex many-body physics across quantum platforms.

We investigate the electromagnetic properties of the fully charm tetraquark states, particularly incorporating contributions from internal gluon radiations. The paper first presents analytical expressions for the next-to-leading-order (NLO) QCD corrections to the decay amplitudes of fully charm tetraquarks into two photons. It is found that the QCD corrections are significant for the $J^{PC}=0^{++}$ fully charm tetraquark decay process, whereas they are relatively small for the $J^{PC}=2^{++}$ fully charm tetraquark decay process. Subsequently, by considering photon-photon fusion in ultra-peripheral high-energy collisions of protons and nuclei and in electron-positron collision processes, we provide theoretical predictions for the production cross sections of fully-charm tetraquark states. The results presented in this work regarding the electromagnetic production and decay of fully charm tetraquarks shall be tested in current and future experiments.