Wegner duality is essential for Z2 lattice gauge theory, yet the duality on non-trivial topologies has remained implicit. We extend Wegner duality to arbitrary topology and dimension, obtaining a new class of Ising models, in which topology is encoded in non-local domain-wall patterns. Without the overhead of gauge constraints, simulating this model on an L*L torus requires only L*L qubits with two-body couplings, halving the conventional four-body coupled 2L*L qubits, enabling full experimental realization of Z2 lattice gauge theory on near-term devices.

The quest to understand three-body dynamics from first-principle QCD includes the study of non-resonant and resonant systems. The isospin $I=2$ system is of particular interest having no three-body resonance but featuring a resonance in a sub-channel, while also being a coupled-channel problem. In this study, we calculate the finite-volume spectrum from lattice QC at two different pion masses, map the amplitude to the infinite volume through a generalized FVU three-body quantization condition, investigate the limit of a narrow $\rho$, and compare with an effective Lagrangian prediction at leading order. Chiral extrapolations between different pion masses are performed.

Gapped two-dimensional gauge theories with massless fermions generically have rich vacuum structures consisting of many degenerate vacua related by the action of topological line operators. The algebra of such operators has been used to calculate ratios of vacuum expectation values of local operators and to predict nontrivial particle-soliton degeneracies. In this paper, we use recently-developed tensor network methods to study several examples of such theories via their Hamiltonian lattice descriptions. Our lattice results agree with all previously-made predictions. Furthermore, we identify the lattice strong-coupling states that can be adiabatically continued to the degenerate vacua in the continuum limit. We conjecture a procedure, referred to as a lattice decay rule, for how this identification works in general. This rule allows us to compute the continuum vacuum degeneracy by studying the lattice Hamiltonian in the strong-coupling limit.

The thermodynamic geometry of the hadron resonance gas model with (without) excluded volume effects (EVE) of baryons is investigated. The case with imaginary mu, where mu is the baryon chemical potential, is investigated as well as the one with real mu. We calculate the scalar curvature R and use the R=0 criterion to investigate the phase structure in the mu^2-T plane where T is the temperature. The curve on which R=0 continues analytically from the imaginary mu region, where the lattice QCD is feasible, to the real mu one. In the presence of EVE, there are rich phase structures in the large real mu region as well as the Roberge-Weiss like region where mu is imaginary and a singularity appears, while there is no phase structure in the large real $\mu$ region in the absence of EVE. The limitation temperature of the baryon gas is also obtained by using the baryon number fluctuation. The LQCD predicted critical point locates almost on the curve of the limitation temperature we determined. A simple sufficient condition, n_B>1/(2v_B)$, is obtained for the quark deconfinement in the large real mu region, where n_B and v_B are the net baryon number density and the volume of a baryon, respectively.

Symplectic quantization is a functional approach to quantum field theory that allows sampling of quantum fluctuations directly in Minkowski space-time by means of a generalized microcanonical ensemble similar to the one of the standard microcanonical approach to lattice field theory. In a previous paper we showed that, for an interacting scalar field theory in 1+1-dimensions, this formalism allows to capture numerically some crucial real-time features inaccessible to any Euclidean approach to lattice field theory. Yet, the new approach was plagued by two main limitations: an ill-defined non-interacting limit and the absence of a direct formal correspondence between its correlation functions and those generated by the Feynman path integral approach. In this paper, we introduce the new \emph{"constrained symplectic quantization"} approach, for which the perfect equivalence with the Feynman path integral is proved and which is perfectly well defined for the free theory. This new approach is characterized by the analytical continuation of all fields and of the action from $\mathbb{R}$ to $\mathbb{C}$ and the presence of some constraints which guarantee the stability of the generalized Hamiltonian dynamics and the convergence of the corresponding generalized microcanonical partition function, hence the name of the theory. We show the application of this formalism to the quantum harmonic oscillator on a Minkowskian-time lattice, finding perfect agreement between one- and two-point numerical correlators and the exact quantum-mechanical results. We observe genuine real-time features such as the oscillatory propagator and the discrete excited-state energy spectrum. Our results provide strong numerical evidence that constrained symplectic quantization can sample real-time quantum-mechanical observables, offering a concrete route to overcome the limitations of Euclidean-time importance sampling.

We develop diffusion models for simulating lattice gauge theories, where stochastic quantization is explicitly incorporated as a physical condition for sampling. We demonstrate the applicability of this novel sampler to U(1) gauge theory in two spacetime dimensions and find that a model trained at a small inverse coupling constant can be extrapolated to larger inverse coupling regions without encountering the topological freezing problem. Additionally, the trained model can be employed to sample configurations on different lattice sizes without requiring further training. The exactness of the generated samples is ensured by incorporating Metropolis-adjusted Langevin dynamics into the generation process. Furthermore, we demonstrate that this approach enables more efficient sampling of topological quantities compared to traditional algorithms such as Hybrid Monte Carlo and Langevin simulations.

Parton distribution functions (PDFs) describe the inner, non-perturbative structure of hadrons. Their computation involves matrix elements with a Wilson line along a direction on the light cone, posing significant challenges in Euclidean lattice calculations, where the time direction is not directly accessible. We propose implementing the light-front Wilson line within the Hamiltonian formalism using tensor network techniques. The approach is demonstrated in the massive Schwinger model (quantum electrodynamics in 1+1 dimensions), a toy model that shares key features with quantum chromodynamics. We present accurate continuum results for the fermion PDF of the vector meson at varying fermion masses, obtained from first-principle calculations directly in Minkowski space. Our strategy also provides a useful path for quantum simulations and quantum computing.

By performing Monte Carlo simulations of the three-dimensional Ising model, we apply the recently proposed Lee-Yang-zero ratio (LYZR) method to determine the location of the critical point in this model. We demonstrate that the LYZR method is as powerful as the conventional Binder-cumulant method in studying the critical point, while the LYZR method has the advantage of suppressing the violation of the finite-size scaling and non-linearity near the critical point. We also achieve a precise determination of the values of the LYZRs at the critical point, which are universal numbers. In addition, we propose an alternative method that uses only a single Lee-Yang zero and show that it is also useful for the search for the critical point.

The hadronic scalar molecules $\mathcal{M}_{b}$ and $\mathcal{M}_{c}$ with asymmetric quark contents $bb \overline{b}\overline{c}$ and $cc \overline{c} \overline{b}$ are explored by means of the QCD sum rule method. Their masses and current couplings are calculated using the two-point sum rule approach. The obtained results show that they are strong-interaction unstable particles and transform to ordinary mesons' pairs. The molecule $\mathcal{M} _{b}$ dissociates through the process $\mathcal{M}_{\mathrm{b}}\to \eta _{b}B_{c}^{-}$. The decays $\mathcal{M}_{\mathrm{c}}\rightarrow \eta _{c}B_{c}^{+}$ and $J/\psi B_{c}^{\ast +}$ are dominant modes for the molecule $\mathcal{M}_{c}$. The full decay widths of the molecules $\mathcal{ \ M}_{b}$ and $\mathcal{M}_{c}$ are estimated using these decay channels, as well as ones generated by the annihilation of $b\overline{b}$ and $c \overline{c}$ quarks in $\mathcal{M}_{b}$ and $\mathcal{M}_{c}$, respectively. The QCD three-point sum rule method is employed to find partial widths all of these channels. This approach is required to evaluate the strong couplings at the molecule-meson-meson vertices under consideration. The mass $m=(15728 \pm 90)~\mathrm{MeV}$ and width $\Gamma[ \mathcal{M}_b] =(93 \pm 17)~ \mathrm{MeV}$ of the molecule $\mathcal{M}_{b}$ , and $\widetilde{m}=(9712 \pm 72)~\mathrm{MeV}$ and $\Gamma[\mathcal{M}_c] =(70 \pm 10)~ \mathrm{MeV}$ in the case of $\mathcal{M}_{c} $ offer valuable guidance for experimental searches at existing facilities.