We present the calculation of the neutron electric dipole moment (nEDM) $d_n$ using 2+1 flavor domain wall fermion ensembles with fixed lattice spacing $a\approx 0.11\,\text{fm}$ and pion masses of 340, 420, and 576 MeV. We show that the neutron electric dipole moment can be extracted from the energy shift induced by a static uniform external background electric field in the presence of the CP-violating QCD theta-term, $\bar\theta Q_{top}$. Motivated by the Feynman-Hellmann theorem, we employ sampling of the topological charge $q_\text{top}(t)$ on a single time-slice rather than the global topological charge $Q_\text{top}=\int q_\text{top}(t) \, dt$, which dramatically improves the statistical precision of the $\theta$-induced nEDM. Key to our method is to calculate the forward matrix element of the topological charge density in the nucleon deformed by a background electric field. We find that calculation with the traditional positive parity-projected nucleon operator is subject to large excited-state contamination. To remove the contamination, we construct the ground state of the deformed nucleon by solving a non-Hermitian generalized eigenvalue problem. With this approach, we find consistent values for the nEDM when using different nucleon interpolating operators, regardless of whether they are covariant or non-covariant under chiral transformations. Finally, after extrapolating to the physical point, we obtain $d_n=-0.0050(4)^\text{stat}(8)^\text{sys}\bar{\theta}$ $e$ fm, where the systematic uncertainty includes excited-state effects estimated as variation with the Euclidean-time fits and the dependence on the strength of the electric field applied to the neutron. Conventional systematic errors like discretization, finite-volume, and chiral extrapolation effects will be addressed in future work.

We study chiral symmetry and singlet $U(1)_A$ symmetry in QCD in a background magnetic field using lattice QCD. We first clarify the neutral-sector symmetry structure in a pure magnetic background, where the unequal electric charges of the light quarks explicitly reduce the non-singlet flavor symmetry. We identify the neutral-pion--sigma susceptibility difference, $\chi_{\pi^0}-\chi_\sigma$, as the chiral-partner splitting associated with the surviving neutral non-singlet axial symmetry, and the neutral-pion--delta susceptibility difference, $\chi_{\pi^0}-\chi_{\delta^0}$, as the singlet $U(1)_A$ partner splitting. We also discuss the disconnected contribution to the neutral-pion susceptibility and its continuum constraint. Numerical results are obtained on fixed-scale $(2+1)$-flavor HISQ ensembles with $m_l=m_s^{\rm phys}/10$, corresponding to a pion mass of about $220~{\rm MeV}$ at vanishing magnetic field. We find that the neutral chiral-partner splitting increases with the magnetic field strength $eB$ at low temperature and decreases at sufficiently large $eB$ near the crossover, providing susceptibility-splitting counterparts of magnetic catalysis and inverse magnetic catalysis, respectively. The singlet $U(1)_A$ partner splitting shows an analogous low-temperature enhancement and large-field suppression near the crossover, with the suppression setting in at larger $eB$ and remaining milder than in the chiral channel. These results provide a first lattice-QCD study of neutral-sector probes of chiral and singlet $U(1)_A$ partner susceptibility splittings in background magnetic fields.

Strong electromagnetic backgrounds make quantum electrodynamics a real-time nonperturbative problem involving dressed fermions and dynamical photons. We propose a trapped-ion protocol for simulating intense-field QED in $3+1$ dimensions in the Furry picture. The construction encodes photon modes in collective phonons and Volkov-dressed fermion modes in ion spins, combining native spin-phonon couplings with Clifford circuits that compress nonlocal Jordan--Wigner strings. For nonlinear Breit--Wheeler pair production, the protocol has polynomial resource scaling and is benchmarked against exact single-mode dynamics with controlled Trotter errors. With experimentally motivated phonon heating and dephasing, zero-noise extrapolation substantially reduces deviations in photon-survival and pair-production signals. These results provide a hardware-efficient route to intense-field particle-production dynamics beyond perturbative or static-field descriptions.

Thanks to bosonization, bosonic lattice models can offer a lattice regularization of chiral fermions. We construct chiral lattice fermion operators in the 2D modified Villain scalar model and evaluate their correlation functions. This microscopic bosonic model has an ultra-local action and an ultra-local symmetry that realizes the fermionic chiral symmetry under bosonization. The reconstructed lattice Dirac operator has no doublers, but is consistent with the Nielsen-Ninomiya theorem because it turns out to be non-local. The non-locality of this derived quantity at finite lattice spacing does not pose any obstructions to gauging the non-anomalous symmetries of the model, which is itself ultra-local.

We establish the multipole structure of the $N \to \Delta$ transition at the level of the generalized parton distributions (GPDs). We decompose the four transition GPDs into one monopole, two dipole, and one quadrupole components in the transverse plane by a multipole expansion of the covariant transition matrix element in terms of the three-dimensional spin-transition tensors and the transverse momentum transfer. These multipole components are in one-to-one correspondence with the light-front helicity amplitudes. In the zero-skewness limit, the multipole GPDs define impact-parameter transition densities, which generalize the transverse transition charge densities to the $x$-dependent level. These transition densities arise from non-diagonal matrix elements between two distinct hadronic states and must therefore be distinguished from the diagonal densities of the nucleon and the $\Delta$. The multipole transition densities visualize the monopole, dipole, and quadrupole structures of the partonic $N \to \Delta$ transition in the transverse plane.

I develop a Hamiltonian framework for ${\mathbb Z}_k$ $p$-form gauge fields on arbitrary oriented cell complexes in arbitrary dimensions. Gauge qudits are defined by $p$-cells, charged boundary qudits by $(p-1)$-cells, Gauss-law generators by boundary map $\partial_p$, and magnetic checks by $\partial_{p+1}$. The same cellular structure produces local dressed Wilson operators, and at $k=2$ a Calderbank-Shor-Steane check complex relevant to quantum error correction. I then specialize to $p=2, k=2$, where the magnetic 3-cell term is absent and the one-form Gauss-law can be solved exactly. The physical Hilbert space is parameterized by plaquette electric-flux variables, while the link configuration is reconstructed as the dynamical boundary of the evolving flux domains. The reduced Hamiltonian is an Ising-type plaquette model, where its local transverse-field term is the physical image of the boundary-dressed Wilson operator $\sigma_p^z\prod_{\ell\in\partial p}\tau_\ell^z$. A tube-cap quench compares two initial flux fillings with the same initial boundary loops. Exact diagonalization on $4\times4$, $6\times4$, and $5\times5$ tori finds that the cap loses $20$-$37\%$ of its occupied-flux area, while the tube remains nearly pinned. A finite-size scaling locates a dynamical crossover of tension-to-density ratio near $(m/\varepsilon_E)_c\simeq1.89$. The unreduced plaquette-plus-link encoding provides local Gauss-law checks and a direct digital implementation, while the reduced plaquette-only Hamiltonian supplies the exact benchmark. The result places the specific top-form discharge and the cosmological constant neutralization calculation inside a general higher-form Hamiltonian and coding framework.

We examine the Lüscher quantization condition to high order for the scattering of a spinless particle and a spin-1/2 particle in a periodic box. First, we derive the quantization conditions in a non-relativistic framework up to total angular momentum $J=11/2$ in both cubic and elongated geometries, and for both rest and moving frames. Then, we introduce a method to transparently cross-check their convergence, using both quantized energy levels in the box and infinite-volume phase shifts for the same potential. We clarify how to incorporate spin-orbit coupling into the formalism and show in detail how the quantization conditions converge order by order in the various irreducible representations. In all, we validated 19 quantization conditions (12 in cubic box, 7 in elongated box). This is a necessary step in applying the method in precision studies of systems in finite volume with half-integer spin, such as meson-baryon scattering.

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 the standard approaches, this construction preserves an exact axial $U(1)$ symmetry at finite lattice spacing. We derive the continuum limit, showing that the model reduces to the \emph{two-flavour} massless Schwinger model, with flavours $\alpha\in\{0,1\}$ sharing one dynamical $U(1)$ gauge field. The central result is a well-defined, regularised, gauge-invariant lattice axial charge $Q_{G}^{A}$ whose continuum non-conservation $\langle dQ_{G}^{A}/dt\rangle = -(2g/\pi)\!\int\! dx\,\langle E(x)\rangle$ arises as a direct dynamical consequence of minimal gauge coupling. A particle-hole transformation on the $\chi$ flavour exposes a hidden $U_{L}(2)\times U_{R}(2)$ chiral symmetry; non-Abelian bosonisation then identifies the model with a massive abelian Schwinger sector tensored with the level-$1$ $SU(2)$ Wess--Zumino--Witten model. Finally, we show that embedding the flavoured fermions in a ribbon-shaped $(2{+}1)$D Bernevig--Hughes--Zhang topological insulator and gauging the bulk in a constant background field factorises the boundary theory into \emph{two decoupled} single-flavour Schwinger models, one on each edge, identifying the lattice factor of $2$ as one quantum of Schwinger anomaly per edge.

We study the Hamiltonian truncation for the two-dimensional $\lambda\phi^4$ theory within the framework of Hamiltonian truncation effective theory, where truncation artifacts are mitigated through a systematic inclusion of corrective terms organized in inverse powers of the ultraviolet energy cut-off $E_{\rm max}$. Building on the leading-order matching program, we develop two complementary extensions. First, we derive compact all-order expressions for the local matching corrections to the mass and quartic coupling by resumming infinite classes of diagrams sharing fixed topologies within the local approximation. Second, we extend the non-local sector by computing the next-to-next-to-local corrections contributing at $\mathcal{O}(E_{\rm max}^{-4})$, following a continuum-first matching procedure, in which the effective corrections are computed in infinite volume and the spatial direction is subsequently re-compactified to obtain a discrete basis of free-Hamiltonian eigenstates on which the truncated operator construction is implemented. Our results show that an increasingly rich operator basis is necessary to describe the theory beyond leading order.