We numerically investigate whether the center-symmetric confined phase of large-$N$ $SU(N)$ gauge theory with one adjoint Dirac fermion persists under spatial compactification on $\mathbb{R}^3 \times S^1$. To this end, we employ a partially reduced twisted Eguchi-Kawai (TEK) model on a $1^3 \times L_4$ lattice with an adjoint Wilson fermion, and measure both the Polyakov loop around $S^1$ and order parameters for volume independence in the reduced directions. For $N=36$, $L_4=2$, $b=0.30\text{-}0.46$, and $\kappa=0.03\text{-}0.16$, we find that, with periodic boundary conditions, the Polyakov loop remains near zero in the light-fermion regime as the circle size is reduced. For the modified twist, the volume-independence order parameters are also consistent with zero in the explored region, supporting the validity of the partially reduced description. These results provide numerical evidence, within the reduced-model setup and parameter range studied, for an adiabatic-continuity scenario in which the confined phase is smoothly connected between large and small circles. By contrast, with antiperiodic boundary conditions, the Polyakov loop exhibits a clear deconfinement transition. We also discuss how this scenario is compatible with the anomaly constraints of the underlying four-dimensional theory. The symmetric twist is examined as a useful comparison, although its volume-independence properties appear less robust at the present value of $N$.

In this paper, we apply the deterministic quantum imaginary time evolution (QITE) algorithm to obtain the ground state of a two-dimensional pure $\mathbb{Z}_2$ lattice gauge theory. We first construct the set of Pauli operators commuting with Gauss's law constraints, generalizing a previous result. This makes the deterministic QITE gauge-invariant and reduces both the measurement and gate costs significantly without adding extra algorithm errors in the QITE. Then, the classical numerical simulation of the deterministic QITE using tensor networks is performed, and the results are compared with the density matrix renormalization group (DMRG) to evaluate the accuracy of the algorithm. Specifically, we investigate the coupling and system size dependence, and find that the deterministic QITE can achieve a relative error of less than $0.1\%$ up to a twelve-plaquette system and coupling values in a regime that we study. Furthermore, the error dependence on the number of time steps is studied and discussed.

We reanalyze the lattice spectra for $I=1/2$ $D\pi$ scattering in the $A_1^+$ irreducible representation from [Phys. Rev. D 111, 014503 (2025)] to investigate the impact of chiral and SU(3) flavor symmetries in $S$-wave $D\pi$ scattering and the $D_0^*(2300)$ resonance. By fitting the phase shifts obtained via Lüscher's formula with both traditional and chirally modified effective-range expansion and $K$-matrix parameterizations, we find that the chiral factor shifts the extracted pole mass closer to the threshold (especially for resonances) and substantially reduces the resonance width. These findings are confirmed by unitarized chiral perturbation theory through a direct fit to the lattice spectra with both the single-channel and the $D\pi$-$D\eta$-$D_s\bar{K}$ coupled-channel schemes. Once the coupled channels are incorporated, the two-pole structure of the $D_0^*(2300)$ emerges. The trajectories of the two poles are investigated by varying the pion mass.

The calculation of resonance form factors in effective field theory as well as on the lattice is a highly challenging task. In a recent paper, we proposed a novel method based on the introduction of a background field and the Feynman-Hellmann theorem to address the problem, and applied it to a toy model. In the present work we use this method for the electromagnetic form factors of the $\rho$-meson. By matching the results to Chiral Perturbation Theory, we provide a first, crude estimate of all three form factors of the $\rho$-meson within the effective field theory. Contact contributions to these form factors turn out to be substantial. A procedure for lattice calculations is outlined, paving the way for an ab initio approach to the problem.

Hadron structure calculations using lattice Quantum Chromodynamics (QCD) have advanced significantly in recent years. Results for charges, form factors, and lower Mellin moments can be obtained to high precision, generalized parton distributions can now be computed either directly or reconstructed from moments, and transverse-momentum-dependent distributions can be accessed through direct lattice calculations. Together, these quantities provide detailed and complementary insights into the internal structure of hadrons. These theoretical developments are highly relevant to the experimental program of the Electron-Ion Collider (EIC) and of other facilities. We review the most pertinent lattice QCD results for hadron structure that inform the EIC scientific agenda, with particular emphasis on the pion, kaon, and nucleon.

We comment on a recent manuscript "Ether of Orbifolds" by Henry Lamm. In the first version, it was mistakenly claimed that the orbifold lattice Hamiltonian is not gauge invariant, and a quantity $\epsilon_g$, which has nothing to do with a non-existent "gauge violation", was introduced. The scaling of this $\epsilon_g$ was used to claim a huge simulation cost. In fact, $\epsilon_g$ characterizes the shift of the effective lattice spacing -- because, in the orbifold lattice formulation, the lattice is generated dynamically from the vacuum expectation value of the complex matrices. In the second version, the claim about the gauge symmetry was partially corrected, based on our comments. However, $\epsilon_g$ is still mistakenly interpreted as a measure of "departure from SU($N$)", inconsistently with the foundational results by Kaplan, Katz, and Ünsal, and also by Arkani-Hamed, Cohen, and Georgi. This interpretation plays a central role in sustaining the argument introduced in the first version.

We introduce the \emph{flavoured lattice Schwinger model}, a $(1{+}1)$-dimensional $U(1)$ lattice gauge theory in which the fermion doubling problem is resolved by staggering a $\mathbb{Z}_{2}$ flavour degree of freedom rather than staggering chirality. Unlike all standard approaches, the flavoured construction preserves an exact axial $U(1)$ symmetry at finite lattice spacing. We derive the continuum limit, showing the model reduces to two copies of the massless Schwinger model labelled by $\alpha\in\{0,1\}$. The central result is that the flavoured construction admits a well-defined, regularized, gauge-invariant lattice axial charge $Q_{G}^{A}$ with chiral anomaly equation $\langle dQ_{G}^{A}/dt\rangle = -(2g/\pi)\int dx\,\langle E(x)\rangle$ in the continuum limit, derived as a direct dynamical consequence of minimal gauge coupling at finite lattice spacing. Restricting to the $\alpha=0$ sector recovers the standard single-flavour result. We further show that spatial separation of the flavour sectors can be realised as a helical edge states living on the boundaries of a ribbon shaped $(2{+}1)$-dimensional Bernevig--Hughes--Zhang topological insulator. This provides a bulk-boundary picture solution to fermion doubling and allows the chiral anomaly to be put on the lattice for a single flavour.

We propose an effective Hamiltonian formulation of quantum field theories using a Daubechies wavelet basis in position space. Combined with flow-equation methods of the similarity renormalization group (SRG), this approach provides an efficient framework for analyzing quantum field theories by reducing the dimensionality of the Hamiltonian and systematically decoupling degrees of freedom across scales. As an application, the free scalar field theory has been reformulated within this framework to calculate the low-lying energy spectrum of the theory. These basis elements are known to transform the free scalar field theory into a theory of coupled localized oscillators, each of which is labeled by a location and a resolution index. In this representation, the Hamiltonian is naturally organized into fixed-resolution blocks, alongside blocks associated with the interactions between different resolutions. To decouple the different resolution modes and obtain a block diagonalized Hamiltonian with each block associated with a fixed resolution, the flow equation approach of SRG is applied. Finally, we demonstrate that with increasing resolution, the low-energy spectrum can be extracted from the effective lowest-resolution block of the Hamiltonian, leading to a significant reduction in computational cost.

In this work we introduce an ansatz for continuous matrix product operators for quantum field theory. We show that (i) they admit a closed-form expression in terms of finite number of matrix-valued functions without reference to any lattice parameter; (ii) they are obtained as a suitable continuum limit of matrix product operators; (iii) they preserve the entanglement area law directly in the continuum, and in particular they map continuous matrix product states (cMPS) to another cMPS. As an application, we use this ansatz to construct several families of continuous matrix product unitaries beyond quantum cellular automata.

We investigate the critical behavior and real-time scattering dynamics of the interacting $\phi^4$ quantum field theory in (1+1)-dimensions using uniform matrix product states (uMPS) and the time-dependent variational principle (TDVP). A finite-entanglement scaling analysis at $\lambda = 0.8$ bounds the critical mass-squared to $\mu_c^2 \in ]-0.2595,-0.2594[$ and provides a quantitative map of the symmetric, near-critical, and spontaneously broken regimes. Using these ground states as asymptotic vacua, we simulate two-particle collisions in a sandwich geometry and extract the elastic scattering probability $P_{11\to 11}(E)$ and Wigner time delay $\Delta t(E)$ using a sandwich geometry protocol. We find strongly inelastic scattering in the symmetric phase ($P_{11\to 11} \simeq 0.712$, $\Delta t \simeq -158$ for $\mu^2 = +0.2$) and almost perfectly elastic collisions in the spontaneously broken phase ($P_{11\to 11} \simeq 1$, $\Delta t \simeq -108$ for $\mu^2=-0.1$ and $P_{11\to 11} \simeq 1$, $\Delta t \simeq -177.781$ for $\mu^2=-0.5$). Crucially, the scattering protocol exhibits a distinctive divergence near the critical coupling; we show that this behavior serves as a dynamical signature of the quantum critical point, arising directly from the closing of the mass gap. These results demonstrate that TDVP-based uMPS can effectively probe nonperturbative scattering and critical dynamics in lattice field theories with controlled entanglement truncation.

We present a comprehensive review of the structure of pseudoscalar mesons within an algebraic model formulated in the light-front framework. The approach provides a unified description of leading-twist parton distribution amplitudes (PDAs), light-front wave functions (LFWFs), generalized parton distributions (GPDs), parton distribution functions (PDFs), elastic electromagnetic form factors (EFFs), charge radii, and impact-parameter GPDs (IPS-GPDs), all derived consistently from the same underlying Bethe-Salpeter amplitudes. Results are discussed for light ($\pi$, $K$), heavy-light ($D$, $D_s$, $B$, $B_s$, $B_c$), and heavy-heavy ($\eta_c$, $\eta_b$) pseudoscalar mesons, allowing for a systematic analysis of the role played by quark-mass asymmetry and heavy-quark dynamics. The study highlights how increasing quark masses drive a transition from broad, asymmetric momentum distributions to increasingly symmetric and spatially compact configurations. Comparisons with lattice QCD, Dyson-Schwinger equation studies, and contact-interaction models are presented where available. Overall, the algebraic model offers a transparent and symmetry-consistent framework to explore the three-dimensional momentum and spatial structure of pseudoscalar mesons across all quark-mass regimes.