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 both the chiral anomaly and fermion doubling.

We present a lattice QCD study of heavy baryons containing charm and bottom quarks, with particular emphasis on the relativistic treatment of all valence quarks. We use $N_f=2+1+1$ HISQ ensembles at the physical point to compute ground-state energies of spin-$3/2^+$ baryons, including singly-, doubly-, and triply-heavy charmed and bottom baryons. This work represents the first investigation of heavy baryons using fully relativistic bottom quarks.

We present a lattice QCD calculation of the electric polarizability of the charged kaon using a four-point function approach, which is the Euclidean analog of low-energy Compton scattering. In the case of the charged kaon, the polarizability is separated into an elastic (Born) term, determined from the charge radius extracted via the kaon electromagnetic form factor, and an inelastic (non-Born) term obtained from the time-integrated difference of four-point correlation functions. Our study employs 500 configurations of Wilson quenched $24^3\times 48$ lattices, and we compute connected diagrams as a proof of principle. From this analysis, we obtain values for the charged kaon electric polarizability of $\alpha_E = (0.988 \pm 0.534) \times 10^{-4}\;\mathrm{fm}^3$ as well as $\langle r_E^2\rangle =0.3303\pm 0.0028\;\mathrm{fm}^2$ for the squared kaon charge radius, after extrapolation to the physical pion mass. The study demonstrates the applicability of the four-point function framework to strange mesons, extends previous four-point function polarizability studies, and provides a foundation for future calculations with increased statistics, dynamical fermions, and improved control of systematic uncertainties.

Quantum Chromodynamics (QCD) at finite density is most often formulated on the lattice as a grand canonical ensemble. Since lattice QCD has a complex action problem at finite baryo-chemical potential ($\mu_B$), its results at finite density are indirect: e.g. in the form of a set of expansion coefficients. In contrast, the canonical formulation offers direct results for integer-valued net-baryon number. In this work we present for the first time results in the canonical formulation with physical quark masses. To this end we use a high statistics finite-volume lattice ($16^3\times8$) data set that we generated at $\mu_B=0$ with our 4HEX staggered action. We extend the canonical ensemble to non-integer net-baryon number and connect the results back to the grand canonical ensemble. Unlike reweighing to real $\mu_B$, this method can also be used with rooted staggered quarks. For densities where the sign problem can be overcome by brute force computing power, this scheme provides lattice QCD results (e.g. for pressure, baryon density) directly, without relying on any extrapolation in the baryo-chemical potential. In this work we chart the phase diagram by studying bulk thermodynamic observables, which we show to be feasible up to $\mu_B\approx500$~MeV.

Theoretical considerations predict a specific hierarchy among ratios of net-baryon number cumulants ($\chi_n$, where $n$ is the order of cumulant) in the vicinity of the transition from the low-temperature hadronic phase to the high temperature quark-gluon plasma phase at small baryon chemical potential, $\mu_\mathrm{B}$, in the QCD phase diagram. This hierarchy, $\frac{\chi_6}{\chi_2} < \frac{\chi_5}{\chi_1} < \frac{\chi_4}{\chi_2} < \frac{\chi_3}{\chi_1}$, has been observed by the STAR experiment in net-proton number (a proxy of net-baryon number) cumulant ratios over a broad range of collision energies. Motivated by these findings, we investigate whether similar ordering emerges generically in finite statistical systems undergoing second-order phase transitions. We employ two different spin models: the two-state and three-state Potts models in two dimensions, both exhibiting a transition from an ordered phase to a disordered phase at their respective critical temperatures. Monte Carlo simulations are performed on square lattices of varying sizes using the Wolff cluster algorithm. Cumulants of the total magnetization are calculated up to sixth order in both of these models in a temperature range near their corresponding critical temperatures. Higher-order cumulants exhibit extrema (peaks/troughs) whose magnitudes grow with both cumulant order and lattice size, reflecting enhanced critical fluctuations. Except within a narrow temperature window above the critical temperature, neither the complete hierarchy nor its exact reverse is realized over the studied temperature range in either model.

Spectral functions play a central role in the characterization of a wide range of physical systems, including strongly interacting quantum field theories and many-body systems. Their non-perturbative determination from Euclidean correlation functions constitutes a well-known ill-posed inverse problem and has motivated the development of numerous reconstruction techniques. In this work, we propose a systematic, prior-free framework for representing spectral functions using an orthogonal functional basis derived directly from the kernel of Euclidean two-point correlation functions. We identify a set of lattice-accessible constraints together with the associated basis functions. These functions can be reorganized into an orthogonal basis within which the spectral function may be approximated in a controlled manner. Using several model spectral functions, we demonstrate that the proposed expansion captures global spectral features and reproduces low-energy transport coefficients with good accuracy. While the numerical implementation requires high-precision Euclidean correlator data, the present framework is intended not as a direct reconstruction method, but rather as a tool for extracting robust constraints and overall spectral structures. The approach may therefore serve as a complementary ingredient or preprocessing step for existing spectral reconstruction techniques.

We propose a $\mu$-dependent coupling for a fractal effective model (FNJL) to make the results for the phase diagram compatible with the experimental data and lattice QCD calculations. The $\mu$-dependence of the coupling, which accounts for gluon effects, is obtained by fitting the lattice QCD results for the pseudo-critical temperature with the fractal model. We then use the new effective coupling in order to compute the dynamical mass, the quark condensate, the thermal susceptibility and, finally, the $T\times\mu$ phase diagram. We consider both extensive and non-extensive statistics, and with a slight variation in the $\mu$-dependent coupling parameters we provide a single result for our model which is able to describe incredibly well the data from STAR, considering the simplicity of the effective model.

We study the impact of background electric fields on a hot plasma of charged particles -- a setting relevant for the early stages of heavy-ion collisions as well as laser pulse experiments. Historically, the electric susceptibility -- encoding the behavior of the hot medium for weak fields -- has been defined within two different formalisms, leading to two distinct results at nonzero temperature. With the help of an exact fermion propagator in a homogeneous electric background field at nonzero temperature and finite volume on the one hand, and an improved perturbative result on the other, we identify the origin of this disagreement. The equilibrium conditions for the system are discussed and the role of the thermodynamic ensemble used to describe the system is highlighted. Finally, we construct the electric susceptibility in a simplified hadron resonance gas model, relevant for the strongly interacting medium in the low-temperature regime.

Several ground state properties of the square-lattice $S=1/2$ Heisenberg antiferromagnet are computed (the energy, order parameter, spin stiffness, spinwave velocity, long-wavelength susceptibility, and staggered susceptibility) using extensive quantum Monte Carlo simulations with the stochastic series expansion method. Moderately sized lattices are studied at temperatures $T$ sufficiently low to realize the $T \to 0$ limit. Results for periodic $L\times L$ lattices with $L \in [6,96]$ are tabulated versus $L$ and extrapolations to infinite system size are carried out. The extrapolated ground state energy density is $e_0=-0.669441857(7)$, which represents an improvement in precision of three orders of magnitude over the previously best result. The leading and subleading finite-size corrections to $e_0$ are in full quantitative agreement with predictions from chiral perturbation theory, thus further supporting the soundness of both the extrapolations and the theory. The extrapolated sublattice magnetization is $m_s=0.307447(2)$, which agrees well with previous estimates but with a much smaller statistical error. The coefficient of the linear in $L^{-1}$ correction to $m^2_s$ agrees with the value from chiral perturbation theory and the presence of a factor $\ln^\gamma(L)$ in the second-order correction is also confirmed, with the previously not known value of the exponent being $\gamma = 0.82(4)$. The finite-size corrections to the staggered susceptibility point to logarithmic corrections also in this quantity. To facilitate benchmarking of methods for which periodic boundary conditions are challenging, results for systems with open and cylindrical boundaries are also listed and their spatially inhomogeneous order parameters are analyzed.