Learned field transformations may help address ubiquitous critical slowing down and signal-to-noise problems in lattice field theory. In the context of an annealed sequence of distributions, field transformations are defined by integrating flow fields that exactly solve a local transport problem. These proceedings discuss a new Monte Carlo approach to evaluating these flow fields, which can then be used directly in such contexts or as a means of generating unbiased training data for machine learning approaches. By defining the Monte Carlo estimator using coupled Langevin noise, the statistical noise in the required integrals is significantly mitigated. Demonstrations of the method include a U(1) transport problem and an SU(N) glueball correlator.

We present preliminary results on the $I=0$, $S=-2$ $H$ dibaryon in $N_{\rm f}=2+1$ QCD. The calculation is performed with heavier-than-physical quarks ($m_\pi \approx 280$ MeV) on a single CLS ensemble. Correlation matrices are constructed using the distillation technique and the three relevant channels, $\Lambda\Lambda$, $N\Xi$, $\Sigma\Sigma$, are investigated to determine the interacting spectrum relevant for $S$-wave across multiple momentum frames. The scattering amplitude is determined by solving the corresponding two-body quantization condition. These preliminary results are part of the ongoing efforts to determine the properties of di-hyperons and to establish whether the $H$ dibaryon exists down to physical quark masses.

Discretization artifacts proportional to the quark mass can limit the precision of strong-coupling determinations in lattice QCD, especially in the presence of heavy quarks. In this work, we perform a lattice perturbative analysis of such $\mathcal{O}(a m)$ effects in the running coupling by computing its two-loop renormalization factor $Z_g$. Using the background field method together with clover-improved Wilson fermions and Symanzik-improved gauge actions, we determine the mass-dependent components of the relevant two-point Green's functions and obtain the improvement coefficients needed to remove $\mathcal{O}(a m)$ artifacts in mass-independent renormalization schemes. Our results are presented for general values of the number of colors $N_c$, the number of quark flavors $N_f$, and the clover coefficient $c_{\mathrm sw}$, and satisfy all symmetry and consistency constraints. Numerical values are provided for widely used instances of the above gauge actions, allowing improved control of mass-related cutoff effects in high-precision determinations of the strong coupling constant from lattice QCD. Full derivations and extended numerical results can be found in Ref. [arXiv:2503.00463].

In this work, we explore a numerical approach for performing the inverse Laplace transformation, with an emphasis on achieving stability and robustness under noisy conditions. Our quadrature-based method integrates reparameterization, data smoothing, and optimization techniques to regularizing ill-conditioned systems. Together, these elements enable consistency checks that enhance the reliability of the inversion process. Through a series of controlled tests on toy models, we demonstrate the stability and effectiveness of the method in the presence of noise. Using mock data, we approximate spectral densities from Euclidean correlators, generating smoothed and stable results that accurately reproduce the correlator behavior, particularly at large Euclidean times. We conclude by discussing prospects for applications to actual lattice QCD data.

Is there a quantum utility in establishing the masses of hadrons? Here we show that the best response is that of Farrés, Capó, and Davis: perhaps, perhaps, perhaps. This is interesting given the general case that particle physics demands quantum computers. For stable hadrons, classical LQCD has achieved sub-percent precision with no sign problem, and quantum computers offer no advantage. For resonances, the Maiani-Testa theorem is an obstruction that quantum simulation is immune to. For nuclei, Wick contractions and signal-to-noise are genuine classical barriers. Underlying these cases is a unified picture connecting the sign problem to Wigner negativity and T gate cost. This manuscript was drafted from extensive interaction with \textsc{Claude}.

We show that a simple qubit-regularized $\mathrm{SU}(3)$ lattice gauge theory (LGT) on a plaquette chain admits a continuum limit with massive glueball excitations, providing a minimal toy model of strong interactions without quarks. By mapping the plaquette-chain Hamiltonian to the three-state quantum clock model in a magnetic field, we demonstrate that the theory can be tuned to a continuum limit governed at short distances by the $\mathbb{Z}_3$ parafermion conformal field theory (CFT), which serves as the ultraviolet (UV) fixed point. A small relevant magnetic perturbation then drives the system to a massive continuum quantum field theory in the infrared (IR). The resulting relativistic massive particles can be interpreted as quasi one-dimensional analogues of glueballs. In the continuum theory we compute the ratio of the lowest glueball masses with opposite charge conjugation to be $m^{-}/m^{+} = \,1.459(2)$ and find $\sqrt{\sigma}/m^{+}\,= 0.2648(2)$, where $\sigma$ is the string tension between a static quark and antiquark.

We investigate the spectrum of doubly charmed tetraquark $T_{cc}$ with quantum number $I(J^P) = 0(1^+)$ using MILC's $N_f = 2+1+1$ HISQ gauge ensembles at two lattice spacings. We have included diquark-antidiquark operator together with molecular and scattering operators in our analysis and varied both the heavy and light quark masses. We employ the anisotropic Clover action for heavy quarks, and $O(a)$-improved Wilson--Clover action for the light (up/down) quarks. In order to handle the non-analyticity near the Left Hand Cut we use modified Lüschers method when close to it.

We report the S-wave interactions between the nucleon ($N$) and the triply charmed Omega baryon ($\Omega_{\mathrm{ccc}}$) using (2+1)-flavor lattice QCD with a physical pion mass ($m_\pi \simeq 137.1$ MeV) on a lattice volume $\simeq (8.1~\mathrm{fm})^3$. The charm quark is implemented with a relativistic heavy-quark action at its physical mass. Employing the time-dependent HAL QCD method, the $N-\Omega_{\mathrm{ccc}}$ potentials in the spin-1 ($^3\mathrm{S}_1$) and spin-2 ($^5\mathrm{S}_2$) channels are extracted. In both channels, overall attraction is found with the scattering parameters, $a_0 = 0.56(0.13)\left(^{+0.26}_{-0.03}\right)$ fm and $r_{\mathrm{eff}} = 1.60(0.05)\left(^{+0.04}_{-0.12}\right)$ fm for the $^3\mathrm{S}_1$ channel, and $a_0 = 0.38(0.12)\left(^{+0.25}_{-0.00}\right)$ fm and $r_{\mathrm{eff}} = 2.04(0.10)\left(^{+0.03}_{-0.22}\right)$ fm for the $^5\mathrm{S}_2$ channel, indicating the absence of a dibaryon bound state. The extracted potentials are further decomposed into spin-independent and spin-dependent components, which provides a useful handle to investigate the underlying interaction mechanism. The spin-independent potential is a dominant component and features a short-range attractive core and a long-range attractive tail, while the spin-dependent potential shows short-range attraction (repulsion) in the spin-1 (spin-2) channel. Qualitative comparisons with previous studies of the $N$-$J/\psi$ and $N-\Omega_{\rm{sss}}$ systems at $m_\pi \simeq 146$ MeV are provided, emphasizing the role of heavy-hadron chromo-polarizability arising from soft-gluon exchange between the nucleon and flavor-singlet hadrons.

Acceptance plenary talk for the 2025 Kenneth G.~Wilson Award for Excellence in Lattice Field Theory: For significant contributions to the understanding of topology in QCD, QCD-like, and large-$N_c$ gauge theories, including algorithmic developments to reduce topological freezing, studies of Dirac spectral properties, and axion phenomenology.

We present new non-perturbative results about the meson spectrum and the low-energy constants of QCD in the 't Hooft large-$N$ limit, $N\to\infty$ with $N_{\scriptscriptstyle{\rm f}}/N\to 0$. These are obtained from lattice Monte Carlo simulations of the Twisted Eguchi-Kawai (TEK) model up to $N=841$. More precisely, we will discuss: our findings for the meson mass spectrum; the determination of the radial Regge trajectories in the $\pi$ and $\rho$ channels; the computation of the coefficients of the $1/N$ expansion of the chiral condensate, of the pion decay constant, and of the next-to-leading-order coupling $\bar{\ell}_4$, up to $\mathcal{O}(1/N^3)$ from the combination of TEK and standard finite-$N$ results.

This study explores confinement-deconfinement transition properties of SU($3$) Yang--Mills theory under weak accelerations at finite temperatures, using first-principles lattice simulations. The system is formulated in the Rindler spacetime, and the properties are studied from the perspective of a co-accelerating observer situated at the center of the lattice. We found that spatially separated confinement and deconfinement phases can coexist in the Rindler spacetime within certain intervals of temperature and acceleration. The position of the boundary between the phases is calculated as a function of temperature for several accelerations, and it is in accordance with the TE prediction, although a small deviation is observed. Moreover, in the weak acceleration regime, the critical temperature of the system is found to coincide with that of non-accelerated gluodynamics.

We present a determination of the bottom quark mass, the masses of S-wave bottom mesons, and their decay constants using an anisotropic clover fermion discretization for the heavy quark, on $2+1$ flavor isotropic QCD ensembles. Our analysis is based on 16 ensembles spanning 6 lattice spacings, with pion masses in the range of 135-350 MeV and several values of the strange quark mass. We demonstrate that the effective anisotropy parameter for the heavy quark approaches unity with controllable $\mathcal{O}(a^2)$ corrections. A non-perturbative renormalization procedure is developed and validated through predictions of the bottom quark mass and decay constants. This framework enables calculations at the physical $b$-quark mass even on lattices with spacing $a \sim 0.1$ fm, where $m_b a \sim 2.5$, while keeping discretization errors in hadronic matrix elements at the $\sim 10$% level which can be eliminated properly through the continuum extrapolation. Using the physical $\Upsilon$ mass as input, we obtain $m_b^{\overline{\mathrm{MS}}}(m_b) = 4.185(37)$ GeV and the full spectrum of S-wave bottom mesons with 0.1% uncertainty or less. Pseudoscalar and vector decay constants and their ratios for all kinds of S-wave bottom mesons are also provided.

The relation between the effective degrees of freedom (EDOF) and the trace anomaly is studied in the hadron resonance gas (HRG) model. If we regard the thermodynamical relation as the evolution equation and define the EDOF as P/T^4, where P and T are the pressure and the temperature, respectively, we obtain the equation which relates to the trace anomaly. The structure of the equation resembles that of the so called c-theorem in the two dimensional conformal field theory which asserts that the EDOF should not increase as the energy scale parameter decreases. There is a stationary point where the trace anomaly (modified trace anomaly) vanishes, and the scale symmetry is restored. To investigate the limiting temperature of the HRG model with the excluded volume effects, we consider two types of the c-theorem like conditions for the EDOF. The first condition requires that the EDOF should not decrease when T increases. This condition is equivalent to the condition that the trace anomaly (modified trace anomaly) should not be negative. The second condition requires that the EDOF should be convex downwards as a function of T. It is found that the first condition gives the limiting temperature of the HRG model with the excluded volume effect which is much higher than the crossover transition temperature obtained by the lattice QCD calculation and, at zero baryon number density, is close to the transition temperature in the pure gluonic theory, while the second one gives the limiting temperature which almost coincides with the one obtained by using the normalized baryon number fluctuation in the previous work and is consistent with the critical point predicted by the lattice QCD calculation.

We explore the finite-density phase diagram of the single-flavour Gross-Neveu-Wilson (GNW) model using matrix product state (MPS) simulations. At zero temperature and along the symmetry line of the phase diagram, we find a sequence of inhomogeneous ground states that arise through a real-space version of the mechanism of Hilbert-space fragmentation. For weak interactions, doping the symmetry-protected topological (SPT) phase of the GNW model leads to localized charges or holes at periodic arrangements of immobile topological defects separating the fragmented subchains: a topological crystal. Increasing the interactions, we observe a transition into a parity-broken phase with a pseudoscalar condensate displaying a modulated periodic pattern. This soliton lattice is a sequence of topological charges corresponding to anti-kinks, which also bind the doped fermions at their respective centers. Out of this symmetry line, we show that quasi-spiral profiles appear with a characteristic wavevector set by the density $k = 2{\pi}{\rho}$, providing non-perturbative evidence for chiral spirals beyond the large-N limit. These results demonstrate that various exotic inhomogeneous phases can arise in lattice field theories, and motivate the use of quantum simulators to confirm such QCD-inspired phenomena in future experiments.

We use lattice field theory to study the finite-volume energy spectrum of the $\pi\pi$ system in $SU(2)$ chiral effective field theory (ChEFT) at leading order in the chiral expansion. \hl{This finite-volume spectrum can be directly related to the (infinite-volume) $\pi\pi$ scattering phase shifts by Lüscher's formula.} We compare our results to the finite-volume spectrum obtained from lattice QCD \hl{by the RBC-UKQCD collaboration}. Our calculation and the lattice QCD calculation are both performed with the physical pion mass and the same \sout{physical volume}\hl{lattice volume (as measured in physical units)}. However, we find significant differences between the two calculations in the isospin $I=0$ channel. In particular, there is a nearly stable $\sigma$ resonance in our lattice ChEFT calculation, which is absent in the lattice QCD calculation. This likely indicates that ChEFT does not converge well with a naive lattice regularization.

We discuss a one-quark state in the confinement phase near a reflective chromometallic boundary both at finite and zero temperature. Using numerical simulations of lattice Yang-Mills theory, we show that the test quark is confined to the neutral mirror by an attractive potential of the Cornell type, suggesting the existence of a mirror-bound one-quark state, a "quarkiton." Surprisingly, the tension of the string spanned between the quark and the mirror is lower than the fundamental string tension. The quarkiton state exhibits a partial confinement: while the quark is localized in the vicinity of the mirror, it can still travel freely along it. Such quarkiton states share similarity with the surface excitons in metals and semiconductors that are bound to their negatively charged images at a boundary. The quarkitons can exist at the hadronic side of the phase interfaces in QCD that arise, for example, in the thermodynamic equilibrium of vortical quark-gluon plasma.

Obtaining hadronic two-point functions is a central step in spectroscopy calculations in lattice QCD. This requires solving the Dirac equation repeatedly, which is computationally demanding. The distillation method addresses this difficulty by using the lowest eigenvectors of the spatial Laplacian to construct a subspace in which the Dirac operator can be fully inverted. This approach is efficient for nonlocal operators such as meson-meson and baryon-baryon operators. However, local multiquark operators with four or more (anti)quarks are computationally expensive in this framework: the cost of contractions scales with a high power of the number of Laplacian eigenvectors. We present a position-space sampling method within distillation that reduces this cost scaling by performing the momentum projection only over sparse grids rather than the full spatial lattice. We demonstrate the efficiency of this unbiased estimator for single-meson, single-baryon and local tetraquark operators. Using Wilson-clover fermions at the $SU(3)$-flavor-symmetric point, we apply this method to study the importance of local tetraquark operators for extracting the finite-volume $T_{cc}(3875)^+$ spectrum. To this end, we extend a large basis of bilocal $DD^*$ and $D^*D^*$ scattering operators by including local tetraquark operators. The inclusion of local operators leads to significant shifts in the estimates of several energy levels. Finally, we show the effect of these shifts on the $DD^*$ scattering phase shift from a single-channel $s$-wave Lüscher analysis.

We report a high precision calculation of the isospin vector charge $g_{S,T}$ of the nucleon using recently proposed ``blending" method which provides a high-precision stochastic estimate of the all-to-all fermion propagator. Through multiplying the current operator by the traditional nucleon interpolator, we create a new operator that captures the major excited state contaminations. The linear combination of this new operator and traditional nucleon interpolator reduces these excited states and improves the robustness of the multi-state fit. Using 15 $N_f=2+1$ lattice ensembles which cover 5 lattice spacing, 5 combinations with the same quark masses and lattice spacing but multiple volumes, including three at the physical pion mass, we report so far most precise lattice QCD prediction $g_T^{\rm QCD} = 1.0264[77]_{\rm tot}(53)_{\rm stat} (13)_{a} (46)_{\rm FV} (01)_\chi (28)_{\rm ex} (04)_{\rm re}$ and $g_S^{\rm QCD} = 1.106[43]_{\rm tot}(31)_{\rm stat} (03)_{a} (28)_{\rm FV} (01)_\chi (08)_{\rm ex} (08)_{\rm re}$ at $\overline{\mathrm{MS}}$ 2~GeV, with the systematic uncertainties from continuum, infinite volume, chiral extrapolations, excited state contamination and also renormalization.

We present a new method for calculating quantum tunneling rates using lattice Monte Carlo simulations in imaginary time. This method is designed with the goal of studying false vacuum decay non-perturbatively on the lattice. We derive a new formula, which is similar in form to Fermi's Golden Rule, which gives the decay rate in terms of an implicit decay amplitude. We then show how to calculate this implicit decay amplitude on the lattice. To deal with the suppression of the false vacuum state in the Euclidean path integral, we develop a new sampling method which combines results from multiple Monte Carlo simulations. For a simple family of one-dimensional quantum systems, we reproduce the tunneling rates calculated from the Schrodinger equation.

We present a key algorithmic improvement to the generalized combinatorial Feynman--Vdovichenko method for calculating the critical temperature of the Ising model on Sierpinski carpets $SC_k(a,b)$, originally introduced in arXiv:1505.02699. By reformulating the method in terms of purely real-valued transfer matrices, we substantially reduce their dimension. This optimization, together with modern computational resources, enables us to reach generation $k=10$ for the canonical $SC_k(3,1)$ carpet. Extrapolation from these data yields the most accurate estimate to date of the critical temperature $T_c^{(3,1)} = 1.4782927(26)$. We further extend the analysis to additional members of the $SC_k(a,b)$ family and report their corresponding critical temperatures.