The Hamiltonian formulation of lattice gauge theories plays a central role in quantum simulations of gauge theories, and understanding their spectrum and other properties is expected to become crucial in the upcoming years. The relevant Hamiltonians in this framework possess local symmetry at each lattice site and may exhibit higher-form symmetries. There are then an exponentially large number of dynamically disconnected symmetry sectors, most of which are not translation-invariant. An exponential number of dynamically disconnected sectors, i.e., Hilbert space fragmentation, can also occur in systems in which no such symmetries have been identified. In this contribution, we describe an emergent gauge symmetry that is valid only in a subset of sectors of the fragmented $S=1$ dipole-conserving spin chain. These non-invertible symmetries can label exponentially many of the model's sectors. Simulating this Hamiltonian, which is not gauge-invariant, yields an exact quantum simulation of a gauge theory.

We discuss the status and progress of recent efforts to modernize the International Lattice Data Grid(ILDG).This includes activities of the metadata and middleware workinggroups concerning deployment and operation of crucial services (user management, metadata catalogues, file catalogues) and extensions of the metadata format, which have been tailored according to the needs of the large collaborations. We also report on developments and extensions that are planned to be addressed in the foreseeable future.

We present a determination of the scalar and tensor $\Lambda\to p$ transition form factors using lattice QCD. These form factors are relevant for semileptonic hyperon decays in the presence of extensions of the Standard Model that include scalar and tensor interactions. The calculation is carried out using a gauge ensemble of twisted mass fermions at the physical pion mass, following the same strategy as our recent study on vector and axial form factors for the same transition. We provide the complete set of form factors as functions of $q^2$ employing a model-independent parametrization. We examine their impact on searches for non-standard charged-current interactions via the muon-to-electron decay-rate ratio $R^{\mu e}=\Gamma(\Lambda\to p\mu\bar\nu_\mu)/\Gamma(\Lambda\to pe\bar\nu_e)$, where scalar and tensor contributions enter linearly and are helicity-enhanced relative to the electron channel. We compare this first-principles prediction for the decay-rate ratio with recent experimental measurements, thereby enabling improved constraints on non-standard charged-current interactions.

We investigate rare special dileptonic decays of $ \Lambda_b$, $\Sigma_b$ and $\Xi_b $ baryons in the Standard Model and context of the general Two-Higgs-Doublet Model with Type III. Specifically, we consider the decays $ \Lambda_b \rightarrow \Lambda \ell^+ \ell^-$, $\Sigma_b \rightarrow \Sigma \ell^+ \ell^-$ and $\Xi_b \rightarrow \Xi \ell^+ \ell^-$, where $\ell$ represents $\mu$ or $\tau$ lepton. By studying these rare decays, we aim to assess the impact of the Two-Higgs-Doublet Model with Type III on various observables, such as the differential branching ratio, total branching ratio, and lepton forward-backward asymmetries using the decay amplitude and the transition matrix elements in terms of form factors calculated via light cone QCD in full theory. We compare our results to those of the Standard Model, as well as existing lattice QCD predictions and experimental data, to assess the agreement and viability of the Two-Higgs-Doublet Model with Type III. Furthermore, we highlight the potential for experimental investigations of these decay channels in the near future. The soon-to-be updated LHCb and/or Belle II detectors, renowned for their capabilities in studying rare decays, present excellent opportunities for probing the predicted branching ratios.

We investigate the properties of neutral and charged mesons in magnetic fields, from weak-field to strong-field regimes. To develop analytic insights, we employ a non-relativistic quark model with a confining potential of the harmonic oscillator type. Short-range correlations, such as Coulomb and color-magnetic interactions, are treated as perturbations. In particular, we focus on the magnetic field dependence of the relative and the center-of-mass motions. The qualitative trends differ significantly between neutral and charged mesons: for neutral mesons, the transverse momenta are conserved and continuous, while charged mesons exhibit quantized transverse dynamics. The Zeeman effects, arising from intrinsic spins and orbital angular momenta, are carefully examined. In particular, for charged mesons with spins $s\ge 1$, we discuss how the zero-point energy in the internal quark motion cancels the Zeeman energy from the orbital angular momentum, ensuring the energetic stability of mesons with high spins. The effectively reduced dimensionality of these mesons in the strong-field limit is also discussed.

Recently, self-dualities based on saddle-point expansions have been proposed as a means to obtain qualitative non-perturbative information in scalar field theories. In this work, we test this proposition quantitatively by studying the phase transition for critical scalar $\phi^4$ field theory in 1+1 dimensions using a variational method. We find that saddle-point methods obtain quantitative agreement for the free energy, but differ on the order of 25 percent for the peak location of the correlation length.

We introduce a method for the selective preparation and detection of quasiparticle wave packets, based on creation operators that generate dressed, localized excitations on top of interacting vacua of (quasi-)one-dimensional quantum lattice theories. This method exploits maximally localized Wannier functions (MLWFs) constructed from quasiparticle bands at intermediate system sizes, enabling the construction of unitary local dressed creation operators. The algorithm allows for species-resolved wave-packet preparation and detection, enabling the separation of known quasiparticle contributions from unknown resonances. We test this approach with matrix product states (MPS) on pure hardcore Hamiltonian QCD on a ladder lattice, detecting scattering outputs and mass resonances.

We consider a quenched SU(2)$\times$U(1) gauge Higgs theory on the lattice, coupled to a static vector-like fermion which, in this case, is in the same gauge group representation as the Higgs field. Physical (i.e. locally gauge invariant) electrically charged and electrically neutral states of matter particles in the electroweak theory were described decades ago, but those constructions do not exhaust all the possibilities, and new types of electrically charged/neutral states, orthogonal to former constructions, are described here. The difference has to do with how the static source, which by itself does not create a physical state, is dressed by dynamical fields. We find that, unsurprisingly, the neutral static fermion is much lighter than any of the charged fermion states. But a lattice study of the propagation of the charged fermion states indicates the existence of (at least) two particle states with different masses in charged particle spectrum.

We address issues related to the presence of defects at finite-temperature topological transitions, in particular when defects are modeled in terms of further variables associated with a quenched disorder, corresponding to the limit in which the defect dynamics is very slow. As a paradigmatic model, we consider the classical three-dimensional lattice ${\mathbb Z}_2$ gauge model in the presence of quenched uncorrelated disorder associated with the plaquettes of the lattice, whose topological transitions are characterized by the absence of a local order parameter. We study the critical behaviors in the presence of weak disorder. We show that they belong to a new topological universality class, different from that of the lattice ${\mathbb Z}_2$ gauge models without disorder, in agreement with the Harris criterium for the relevance of uncorrelated quenched disorder when the pure system undergoes a continuous transition with positive specific-heat critical exponent.