A recent non-perturbative formulation of $2n$ dimensional chiral gauge theories relies on realizing chiral fermions on the $2n$ dimensional boundary of a $2n+1$ dimensional disk manifold. It also requires extending boundary gauge configurations into the interior of the disk using some flow prescription that preserves 2n dimensional gauge invariance. In this paper we propose a concrete realization of the equation of motion flow with the disk embedded on a square lattice. In addition, we couple the flow gauge field to fermions and demonstrate the mechanism of anomaly inflow and anmaly cancellation at work on the lattice.

The proposal to formulate chiral gauge theories using domain wall fermions on $2n+1$ dimensional Euclidean lattice with a slab geometry involves $2n$ dimensional dynamical gauge fields residing on one of the domain walls. The gauge fields are extended into the extra dimension using gradient flow decoupling the mirror fermions on the anti-wall. We implement this construction on the lattice for $n=1$ in the presence of $2n$ dimensional background gauge fields. We also formulate and implement an additional gauge field flow proposal, where the gauge fields satisfy $2n+1$ dimensional equation of motion away from the domain wall, known as the EOM (equation of motion) flow. In both cases, we couple the gauge fields to fermions and demonstrate how current conservation and anomaly inflow work on the lattice.

We present a continuous-variable adaptive variational quantum eigensolver (CV-ADAPT-VQE). As concrete examples, we consider the ground-state preparation for (i) the Bose-Hubbard model and (ii) the bosonic Kitaev chain, including its extension with an on-site Kerr interaction. The former conserves the total boson number, while the latter conserves global parity. We construct symmetry-preserving operator pools tailored to each case and show, using GPU-based classical simulations, that CV-ADAPT-VQE results in significantly shallower circuits compared to Hamiltonian-based VQE approaches. Our results point toward direct applications in quantum simulations of condensed-matter systems, quantum chemistry, and high-energy physics.

We perform detailed studies of five Hamiltonian variational ansatzes (HVA) based on the Hamiltonian of the $(1+1)$d $\mathbb{Z}_2$ lattice gauge theory. The ansatzes are designed to respect local and global symmetries of the original Hamiltonian and therefore act on a finely segmented state Hilbert space. Following Larocca et al. (2023), we numerically study the dimension of the dynamical Lie algebra (DLA) and the rank of the quantum Fisher information matrix (QFIM) of the ansatzes within specific invariant subspaces. The ansatzes all involve sums of weight-three Paulis in their generators, which is a feature that have so far been underexplored in this context. We also perform numerical experiments to determine the ground state energy of the original Hamiltonian via variational quantum eigensolver (VQE), and observe that overparametrization of the ansatzes coincides with the apparent disappearance of local minima in the loss function, in line with the finding in the reference. Finally, the decay rate of the VQE loss function under gradient descent optimization is revealed to scale linearly with the number of parameters in the ansatz. These results help to enrich the theory of overparameterization of quantum circuits and inform the design of scalable variational ansatzes.

The spectrum of vector charmonium(-like) states in the 4.1-4.6 GeV energy region exhibits a long-standing tension. While the inclusive $R$-value indicates the presence of only vector charmonia that are usually interpreted as conventional states, exclusive $e^+e^-$ cross sections reveal additional structures whose parameters strongly depend on the observed final states when fitted with Breit-Wigner functions. This puzzling pattern suggests that coupled-channel and threshold effects play an essential role. In this work, we develop a unified coupled-channel framework relevant for the $1^{--}$ resonances in the considered energy region. The framework incorporates the $S$-wave open-charm channels $D\bar{D}_1$, $D^*\bar{D}_1$, and $D^*\bar{D}_2^*$, constrained by heavy-quark spin symmetry, optional bare poles corresponding to quark-model states which may be associated with the $\psi(4160)$ and the $\psi(4415)$, and final-state interaction in the $Z_c$ channels relevant for the three-body final states. We employ several benchmark models based on the constructed framework to perform simultaneous fits to the BESIII data for the cross sections of $e^+e^-\to J/\psi\pi^+\pi^-$, $h_c\pi^+\pi^-$, $D\bar{D}^*\pi$, $D^*\bar{D}^*\pi$, $J/\psi\eta$, and $\chi_{c0}\omega$, together with the available invariant-mass distributions that exhibit the $Z_c(3900)$ and $Z_c(4020)$ structures. The models differ in the number of bare seed states and the fitting strategy. We show that even the purely dynamical scheme captures the gross features of all the analyzed distributions. We therefore conclude that the nontrivial behavior of the measured line shapes in the studied energy range can be understood in terms of strong coupled-channel effects with dynamically generated poles. The inclusion of bare compact states leads to a quantitative improvement of the fit quality but does not alter this conclusion.

We propose a statistical-field framework for text generated by large language models (LLMs), treating token embeddings as continuous spin variables on a one-dimensional chain. Defining a susceptibility from the connected two-point correlator and an order parameter from the ensemble-averaged embedding field, we vary the \texttt{softmax} temperature $T$ and observe a sharp susceptibility peak near a characteristic $T_c$ with power-law-like scaling, a concurrent rapid change in the order parameter, and a collapse onto a single semantic direction below $T_c$. The intrinsic dimension estimated by the two nearest neighbor (TwoNN) method independently corroborates these findings, reaching a minimum near $T_c$. Results are robust across model scales (Qwen3: 0.6B--32B) and prompt categories. While the phenomenology closely resembles a continuous phase transition, the non-equilibrium nature of autoregressive generation warrants further investigation. Our framework provides quantitative tools for probing the collective statistical structure of LLM outputs and suggests connections between decoding strategies and critical phenomena.

We define a finite-volume lattice-QCD density-matrix observable for the vacuum-subtracted spatial R'enyi response of a source-sink-prepared, momentum-projected hadron. At fixed regulator, integer R'enyi index $n>1$, spatial region $B_R$, spin projection, gauge-theory cut prescription $\mathcal{C}$, and after the usual double-sided source-sink projection, the central result is an exact source-sink replica identity: the response is obtained from the logarithm of a replicated hadron correlator on the cut geometry normalized by the corresponding power of the ordinary one-sheet correlator. This identity makes the natural first numerical target the two-sheet $n=2$ measurement of the replicated source-sink correlator ratio, together with a finite-volume test of whether the response scales as $L^{-3}$ at fixed physical $R$. The exponent is a lattice output to be tested, not an input theorem for the nonlinear R'enyi functional. The construction is prescription-defined in gauge theory, and full QCD requires the replicated sea-quark determinant and valence contractions on the replicated cut graph; quenched and partially quenched calculations are therefore pilots. Large-$N_c$ two-dimensional QCD provides an interacting benchmark in which the matched one-meson response is suppressed by the inverse spatial volume, with the short-interval coefficient controlled by light-front PDF moments.

Deeply virtual meson production (DVMP) is among the most prominent channels to extract the nucleon's generalized parton distributions (GPDs) at $ep$ scattering facilities such as {\tt JLab} and the upcoming {\tt EIC/EicC} experiments, which plays a vital role in unravelling the three-dimensional internal structure of nucleon. In this work we calculate for the first time the next-to-next-to-leading order (NNLO) QCD radiative corrections to the DV$\pi$P processes $\gamma_L^* p\to \pi^+ n$ and $\gamma_L^* p\to \pi^0 p$ in the generalized Bjorken limit $Q^2\gg \vert t\vert, \Lambda_{\text{QCD}}^2$, accurate at the leading twist within collinear factorization framework. The impact of the two-loop QCD corrections appears to be positive and substantial, including which considerably improves the agreement between the perturbative QCD prediction and the available {\tt JLab} data. In addition to the differential longitudinal DV$\pi$P cross section, we also study the impact of the two-loop QCD corrections on the transverse single-spin asymmetries (TSSA) in some benchmark kinematics at {\tt JLab}, {\tt EIC} and {\tt EicC}.