Papers

Imaginary-time evolution can be reconstructed from real-time quantum simulations using exact integral transforms. We identify the construction of Guo, Shibu, Lin, and Zhao as a continuous linear combination of Hamiltonian simulations and show that its slow $1/t_{\rm cut}$ convergence arises from a redundant kernel component. We extend the construction from pure-state matrix elements to thermal traces and correlators. One real-time dataset then reconstructs targeted inverse temperatures, Euclidean separations, and chemical potentials through classical post-processing, bringing finite-$(T,\theta,\mu)$ physics within reach of real-time quantum simulation without thermal-state preparation. We benchmark the method on one- and two-flavor lattice Schwinger models, including circuit-level simulations with depolarizing noise.

We extend a lattice-QCD determination of the response of the quark-gluon plasma to an external magnetic field using a Taylor expansion of the pressure at zero field. A zero-net-flux “half-and-half” magnetic-field configuration permits continuous differentiation with respect to the field amplitude on gauge ensembles generated at $B=0$. The electromagnetic vector potential is chosen to minimize stochastic noise in the Taylor operators. Previous results through $O(B^2)$ are extended to $O(B^4)$ using $2+1$-flavor HISQ/tree ensembles with $m_l/m_s=0.05$ and $N_t=8$. The renormalized quadratic coefficient confirms paramagnetic behavior above the QCD crossover. The fourth-order coefficient $C_4$ is small at high temperature and is enhanced near the crossover. At $T=167$ MeV the $C_4$ result at $48^3\times 8$ lies about two standard deviations above the corresponding $32^3\times8$ one, indicating likely finite- volume effects. For $eB = 0.2$ GeV$^2$, characteristic of magnetic fields relevant to heavy-ion phenomenology, the fourth-order contribution is small compared with the leading magnetic correction at moderate and high temperatures, but near the crossover the large-volume result is about half of the central value of the quadratic term, after the vacuum-pressure subtraction. We also place the method in the context of other lattice determinations of magnetic susceptibility and clarify the relevance of finite-volume effects for the thermal subtraction. This work was completed in 2014 and preliminary results were reported at Lattice 2014.

Constructing hadron creation operators which properly sample the finite-volume energy spectrum is a fundamental step in lattice QCD spectroscopy and scattering calculations. Operators enabling access to spectrum information from correlation functions at early temporal separations are extremely advantageous, particularly when the signal-to-noise problem is severe. We present improved operator constructions for charmonium, glueball and baryon spectroscopy which exhibit these advantages. Novelties of our work include the extension of the distillation profiles framework to baryon and multi-meson calculations, as well as an efficient implementation of glueball-like operators which retain angular momentum information from the continuum.

We study the ferromagnetic Ising model on finite hyperbolic tessellations of Euclidean AdS$_2$ with open and wired boundary conditions. Because a finite fraction of spins remains at the boundary as the lattice grows, these conditions select distinct thermodynamic behaviours. In the $\{5,4\}$ tessellation, Monte-Carlo simulations using efficient worm algorithms on open boundaries (OBC) yield a transition near $\beta_c J=0.632(3)$, with susceptibility data collapsing under scaling by the total number of spins $N$. The fitted finite-size exponents, $1/\bar{\nu} \simeq 0.162$ and $\gamma/\bar{\nu} \simeq 0.743$, differ substantially from the mean-field volume scaling. Wired boundaries (WBC), which correlate boundary spins, instead show a transition around $\beta_c J=0.348(4)$ to an ordered phase consistent with the mean-field exponents. While the mean-field criticality with WBC is consistent with previous studies and with the suppression of independent boundary fluctuations, the OBC exponents hint at the presence of a new universality class. Results from other tessellations support the robustness of the observed scaling with OBC. We discuss a possible route to interpolate between the different boundary conditions. Our findings show that boundary dynamics must be specified when characterizing critical behaviour on hyperbolic lattices.

We present preliminary results obtained in the first extensive study of the Möbius domain wall fermion (MDWF) lattice formulation of the four-dimensional Sp(4) gauge theory coupled to two dynamical fermions transforming in the fundamental representation. This theory is important for extensions of the Standard Model, as it provides the microscopic origin for both composite Higgs and dark matter models based on the SU(4)/Sp(4) coset. We scan the space of bare lattice parameters, including those entering the MDWF, and monitor spurious effects, such as the residual mass. We identify optimised regions of parameter space in which lattice artefacts affecting the global symmetries of the theory are suppressed. We then perform preliminary measurements of the lightest pseudoscalar and vector meson masses, together with the pseudoscalar decay constant. We demonstrate the potential of the MDWF formulation to enable continuum-limit extrapolations with reduced lattice discretisation effects.

Disconnected diagrams remain a major challenge for precision lattice QCD calculations because of their large statistical fluctuations. We investigate a subtraction method based on a domain decomposition of the Dirac operator, yielding a biased but substantially less noisy estimator. Applying the method to charmonium disconnected correlators computed using distillation, we achieve a variance reduction of about three orders of magnitude at only twice the computational cost, providing a practical alternative to completely neglecting disconnected contributions.

Against a background supported by the three pillars of emergent mass, this contribution challenges the fidelity of vector meson dominance as an instrument for relating the electromagnetic vector-meson (V) production reaction $e + p \to e^\prime + V + p$ to the hadronic process $V + p \to V + p$. It also describes a viable reaction model for exclusive photoproduction of light and heavy vector mesons from the proton, which exposes the $q\bar q$ content of the photon. That model's successes reveal that it is premature to link extant $V + p \to V + p$ data with, for instance, in-proton gluon distributions, the QCD trace anomaly, or pentaquark production. Improved reaction theory and more precise data are required before the validity of such links can objectively be assessed.

We make use of unique properties of scaling functions to estimate the chiral phase transition temperature and corresponding universal critical parameters of this phase transition directly from (2+1)-flavor QCD simulations with highly improved staggered fermions on lattices with temporal extent $N_\tau=8$. Working with an improved chiral order parameter for quantifying chiral symmetry breaking, we analyze the finite-volume dependence of this observable for a wide range of lattice volumes and light quark masses, and quantitatively estimate the deviations from the expected universal scaling behaviour as a function of the light-to-strange quark mass ratio.

Lattice gauge theories are an important class of physical models with high-dimensional structured distributions that underpin first-principles calculations in particle, nuclear, and condensed-matter physics. Recent advances in generative modeling have opened new avenues for sampling Boltzmann distributions in lattice gauge theories, offering the potential to alleviate limitations of traditional Monte Carlo methods, including critical slowing down and topological freezing. However, generative samplers for lattice gauge theories are typically constructed in link space, where correlations become increasingly long-ranged toward weak coupling, posing a challenge for learning. Plaquettes provide a more natural representation, as the action is local in these variables. However, exact Bianchi constraints restrict them to a lower-dimensional manifold, complicating direct generative modeling. We introduce a multilevel normalizing-flow construction that samples directly in plaquette space while satisfying these constraints exactly. The key idea is a coarse-to fine factorization that transforms a globally coupled constraint problem into a sequence of local solves: at each refinement, every determined plaquette depends on at most four newly generated variables, while the size of the constraint problem remains independent of the lattice size. We validate the construction for $U(1)$ in two and four dimensions and for $SU(2)$ in two dimensions. Our multilevel Plaquette-Space Sampler (PSS) substantially outperforms link-space baselines, with the advantage increasing toward weak coupling, where the gauge coupling becomes small. This regime is particularly challenging for generative sampling and, in asymptotically free gauge theories, is relevant to continuum studies.

We analyze the out-of-equilibrium relaxational dynamics of ferromagnetic Ising-like systems driven across their low-temperature magnetic first-order transition (FOT) line, by sudden and slow variations of an external homogenous magnetic field $h$. As a paradigmatic example, we consider a two-dimensional Ising system driven across its low-temperature FOT line by suddently quenching $h$ from $h_i<0$ to $h>0$, inducing a transition from the negatively to the positively magnetized phase. We show the emergence of a dynamic percolation transition at a finite critical time $t_c(h)$ along the post-quench evolution for finite (sufficiently small) values of $h$, which is marked by the percolation of the largest positive-spin cluster and the antipercolation of the largest negative-spin cluster. This out-of-equilibrium percolation transition displays a finite-size scaling behavior as in the standard random-percolation case. However, while the fractal dimension of the percolating clusters is consistent with the random-percolation value, the exponent controlling the approach to criticality differs and depends on $h$. We also show that the percolation transition marks the passage from the metastable negatively-magnetized phase to the stable positively-magnetized one. Therefore, in the small-$h$ limit, the percolation critical behavior is related to the spinodal-like behavior of the magnetization, implying that the percolation time $t_c(h)$ exhibits a spinodal-like exponential dependence on $h$. The existence of percolation transitions is likely a generic phenomenon at magnetic Ising-like FOTs. For example, we observe an analogous behavior in dynamic (Kibble-Zurek-like) protocols entailing slow variations of the magnetic field driving the crossing of the FOT line.

We use lattice gauge theory to investigate the Peskin-Takeuchi S parameter in SU(3) gauge theory with eight light fundamental fermions (eight-flavor QCD), a candidate for walking technicolor. We develop a new approach to computing S using the first time moment of current correlators, in addition to the conventional vacuum-polarization method, and obtain consistent results. Finite-volume (FV) corrections are estimated using data at multiple lattice volumes and a formula motivated by chiral perturbation theory. At the smallest fermion mass, the one-doublet contribution is S = 0.281(5)(17), smaller than the value $\sim 0.35$ in scaled-up 2+1-flavor QCD (without subtracting the SM contribution). However, contrary to naive expectations, S toward smaller fermion masses is not necessarily suppressed once FV corrections are included. The resulting Gasser-Leutwyler parameter $L_{10}^r(M_\rho)$ is similar to that in real-world QCD. We also determine the vector and axial-vector meson decay constants, $F_\rho$ and $F_{a_1}$. The ratio $F_\rho/F_\pi$ is stable against the fermion mass and consistent with the KSRF estimate, implying a $\rho\pi\pi$ coupling similar to that in real-world QCD. We predict the techni-rho decay width into weak bosons to be $\Gamma_\rho/M_\rho \lesssim 0.24/N$, where N is the number of weak doublets. We further find that the rho- and $a_1$-dominated Weinberg spectral-function and Das-Mathur-Okubo sum rules are satisfied, yielding S and $L_{10}^r(M_\rho)$ consistent with our main results. We discuss implications for BSM model building.

The inclusion of isospin-breaking corrections arising from electromagnetic interactions and the up-down quark mass difference is becoming increasingly important in lattice QCD calculations, as the precision of observables is at or approaching the percent level. In this context, the RM123 method has been employed in recent years to take into account such isospin corrections. In this work, we study baryon mass splittings using the RM123 approach. Preliminary results are presented for the mass splittings within spin-1/2 and spin-3/2 baryon SU(2) multiplets, obtained using twisted-mass ensembles tuned close to physical quark masses. We consider only valence contributions, with the splittings computed at leading order in the isospin-breaking parameters.

We distinguish two Casimir observables associated with a conformal surface defect. A circular cylinder embedded in flat space has a logarithmic contribution to its Casimir energy, $-d_1\log(R/\epsilon)/(24R)$, fixed by the displacement anomaly. A great cylinder obtained by radial quantization of the ambient theory instead has Casimir energy $-b/(12R)$ in the conformal defect vacuum with a fixed local anomaly convention. Free-field and holographic calculations provide checks of the proposed relations in both embeddings.

We present a systematic study of the ground states of pentaquark systems using the neural network variational Monte Carlo method within the constituent quark potential model. We investigate all manifestly exotic pentaquark systems with negative parity, which cannot mix with the conventional baryons through the creation and annihilation of light or strange quark pair. We exhaust 387 color, spin, and isospin configurations and identify 21 pentaquark bound state candidates with binding energies ranging from $2$ to $15$ MeV. A striking observation is that all of the bound states are shallowly bound molecular states, and a deeply bound pentaquark state does not exist. The $QQqq\bar{Q}$, $ssqq\bar{Q}$, $Qsqq\bar{Q}$ and $Qqqq\bar{Q}$ bound states are composed of a heavy vector meson and a baryon, while the $QQqq\bar{s}$ and $Qqqq\bar{s}$ bound states are composed of a $K$ meson and a heavy baryon. As a cross-validation, the ground-state energies of the unbound systems converge to the baryon–meson thresholds from above, which are consistent with the S-wave scattering states and provide a reliable baseline for the bound-state criterion. Especially, we reproduce the lowest scattering states $\eta_c N$ and $\eta_c \Lambda$ in the $qqqc\bar{c}$ and $qqsc\bar{c}$ channels respectively, where the hidden-charm pentaquark resonances were observed experimentally. We also find that all fully heavy pentaquark states are unbound. Our results provide valuable guidance for future pentaquark searches at LHCb, Belle II, and other experiments.

Efficient sampling from Boltzmann distributions is central to modelling complex physical systems. Markov Chain Monte Carlo (MCMC) methods suffer from critical slowing down, high autocorrelation, and poor mode-mixing, limiting their scalability. Recent advances, like Boltzmann Generators, offer a promising alternative but remain constrained by costly MCMC-based training, inefficient sampling, and poor ergodicity. We introduce an algorithm for learning Boltzmann distributions that does not require any true samples for training. Our approach draws inspiration from flow matching but departs fundamentally from sample-trajectory matching to distribution-trajectory matching. The algorithm iteratively reshapes the target distribution, using model generated samples to guide learning and ensure comprehensive mode coverage. We validate our method on standard benchmarks, including a 2D Gaussian mixture, Many-Well distributions, and high-dimensional scalar $\phi^4$ theory. The proposed approach not only improves sampling performance and accuracy over traditional MCMC and flow-based baselines but also establishes a new method for sample-free learning of complex physical distributions.

Efficiently learning and sampling from high dimensional, multimodal unnormalized distributions without target samples remains a challenging problem. Although normalizing flows can generate samples efficiently, training based on the reverse KL divergence using only the unnormalized target density may suffer from mode collapse. We introduce SIMANF, a sample free framework that integrates simulated annealing with normalizing flows. SIMANF progressively transforms the target distribution from a smooth initial form to the original target distribution and trains the flow sequentially across these stages. By transferring the learned representation between stages, the method promotes mode coverage while progressively capturing finer features of the target distribution. Following annealing, a final refinement stage combines the reverse KL divergence with an importance weighted forward KL objective using samples generated by the flow. SIMANF requires no target samples during training and uses only the unnormalized density. We demonstrate its effectiveness on Many-Well distributions and high dimensional Scalar Phi4 lattice field theory distribution.

Large-momentum effective theory (LaMET) provides a first-principles framework for computing the $x$ dependence of light-cone parton distributions from lattice QCD. Over the past decade, theoretical and numerical advances have established a mature multi-stage workflow for systematic calculation of parton physics, although its implementation still requires expert judgment and substantial repeated effort. We present lamet-agent, an open-source large language model (LLM) agent framework that organizes this workflow into an executable, reproducible, and inspectable analysis pipeline. The present release supports collinear quark distributions and implements correlator analysis, renormalization, Fourier transformation, perturbative matching, continuum, physical pion mass and infinite-momentum extrapolations, and automated result review. We validate it on four end-to-end analyses: pion parton distribution functions in the gauge-invariant and Coulomb-gauge formulations, and pion and kaon distribution amplitudes, obtaining results consistent with the published calculations. Extensions to transverse-momentum-dependent distributions, generalized transverse-momentum-dependent distributions, and gluonic distribution functions are planned for subsequent releases.

We report the first quantum-hardware implementation of Real-time Estimators for Scattering Observables (RESOs). The physical model is a one-dimensional lattice theory of non-relativistic spin-1/2 fermions with a single contact interaction. The lattice sizes studied are up to $N_x=54$ lattice sites and up to $20$ time steps. Spacetime correlation functions were computed on IBM's quantum computers, using $109$ qubits with $10,806$ CZ gates applied, reaching a two-qubit gate depth of $246$. We demonstrate how to study bound states and extract scattering amplitudes from these correlation functions.

We study the spectrum of two-dimensional Yukawa theory using Hamiltonian truncation, with a focus on bound states. We extend the framework of Hamiltonian truncation effective theory to include fermions and logarithmic UV divergences. With these corrections, the energy levels converge as a function of the cutoff with the scaling predicted by power counting. We identify a strategy to follow the evolution of fermion-antifermion bound states from weak to strong coupling, and investigate its binding energy, finding good agreement with finite-volume perturbation theory at weak coupling. Finally, we explore the heavy-scalar regime toward the massive Thirring/Sine-Gordon limit, recovering the expected weak-coupling behavior and outlining how the calculation can be extended toward this limit.

The Quantum Approximate Optimization Algorithm (QAOA), whose design is underpinned by the adiabatic theorem, is one of the leading variational quantum algorithms for preparing the ground states of gauge theories. A recently proposed variant, DC-QAOA, incorporates counterdiabatic driving to accelerate the adiabatic process, reducing both circuit depth and runtime. In this work, we present a systematic analysis, from both theoretical and computational perspectives, of DC-QAOA and related counterdiabatic variants for preparing the ground state of the Schwinger model, the paradigmatic (1+1)-dimensional lattice gauge theory. Benchmarking these methods against standard QAOA, we show that counterdiabatic driving improves ground-state preparation while lowering circuit depth requirements. Our results establish counterdiabatic protocols as a practical route towards efficient quantum simulation of gauge theories.

Existing quantum simulations of the two-flavor Schwinger model have run at a single lattice size, and it is not known how far the variational approach can be pushed or which weakness stops it first. Following the model from N = 2 to 6 staggered lattice sites, we find that the binding constraint at reachable sizes is hardware noise rather than circuit expressibility or trainability, and identify N = 3 as the immediately viable extension of existing trapped-ion experiments. The energy error of a charge-conserving ansatz collapses onto one function of p/d, the ratio of variational parameters to physical-sector dimension, and falls by more than two orders of magnitude as p/d rises through order unity, giving the expressibility condition L(4N - 1) >= binom(2N,N) for L circuit layers. The condition is local in chemical potential: at N = 3 the layer count sufficient at zero chemical potential leaves a 74.38% error near the first-order boundary, while one further layer reaches 0.08%. Charge conservation also protects trainability and prevents charge-sector leakage: as the qubit count doubles from 4 to 8, the normalized gradient variance falls to 1/3.56 of its starting value for the constrained ansatz, versus 1/13.57 for an unconstrained circuit. Comparing a global contraction with per-gate local noise, a fixed-parameter control shows that the noise model, not whether the optimizer runs inside the noisy loop, sets how strongly noise degrades the first-order transition. At N = 4, a noiseless control reaches 0.12% mean error, whereas the same circuit at 1.00% depolarizing noise reaches 25.69 to 52.81%.

A new proposal called DM-SMC (Diffusion Model - Sequential Monte Carlo) is investigated, which samples ensembles defined in terms of an action, using diffusion models trained on samples from the ensemble. The SMC setup allows for accurate sampling in spite of an approximate diffusion model and the finite stepsize used in the numerical solution of the stochastic process. Improved update strategies are also investigated. Results are presented for a $Z_2$ symmetric scalar field theory in 2 dimensions near its 2nd order phase transition.

Quantum computing offers a new, orthogonal direction for investigating fundamental physics, extending beyond classical numerical methods and conventional observables. Realizing this potential requires directly confronting the noise limiting currently available quantum computers. Progress rests on advancing algorithms, interpreting their results, and managing their errors together. This thesis presents several advancements in the use of quantum simulation and quantum information to probe fundamental physics. The first is in the use of quantum computers to simulate collisions in quantum field theories. Central to these simulations are new wavepacket preparation, time evolution, and error mitigation techniques, which allow for simulations with some of the largest effective circuit volumes to date. These methods enable the first quantum simulation providing numerical evidence for inelastic particle production, a key process in fundamental physics. The second advancement centers on the role quantum-information-theoretic quantities play in physical processes. Beyond mere correlations with the physics of the process, entanglement and magic are shown to probe the interactions present in scattering and hadronization dynamics. A precision study requires a complete quantification of algorithmic and hardware uncertainties, an outstanding goal as quantum simulations mature. The third advancement in this thesis addresses error management. A framework minimizing the effect of algorithmic errors in analog quantum simulations is presented. In a step toward fault tolerance, error detection in encoded quantum simulations is shown to improve estimation of local observables relative to unencoded runs. Together, the developments in this thesis mark practical progress toward fault-tolerant quantum simulations of fundamental physics capable of scientific discovery.

Key properties of a large sparse operator can often be determined by only a small, spectrally localized subset of its eigenmodes. In lattice QCD with Wilson fermions, the sign of the fermion determinant is determined by the parity of the number of eigenvalues lying on the negative real axis of the non-Hermitian Wilson-Dirac operator. Determination of this signature can be challenging, particularly in parameter regimes where near-zero modes can lead to exceptional configurations. We present a contour-integral-based spectral projection method to count the negative-real eigenvalues of the non-Hermitian Wilson-Dirac operator $D$ that determine the sign of its determinant. The spectral projection is supplemented by an adapted deflation-accelerated solver for shifted linear systems and singular-value exclusions to reliably set spectral bounds and contour boundaries. We demonstrate the robustness of the method through systematic convergence tests, including variations of the contour size, and show its ability to resolve eigenvalues close to the negative real axis. Beyond fermion determinant sign evaluation, the approach provides a systematic means of isolating physically relevant eigenvalues embedded in dense complex spectra, with potential applications to non-Hermitian quantum systems, stability analyses, and large-scale eigenvalue problems.

We study non-stabilizerness (magic) in the ground state of $(2+1)$-dimensional $\mathrm{SU}(2)$ Hamiltonian lattice gauge theory with matter, formulated in the dressed-site basis in the hardcore-gluon truncation and restricted to the zero baryon-number sector. Using matrix product states, we compute three facets of magic: the second-order stabilizer Rényi entropy (SRE) $M_2$, its non-local component $M_2^{\rm NL}$, and a lower bound in terms of the anti-flatness $F$ of the entanglement spectrum. We also prove a stronger form of the sandwich relation: $-\log_2(1-4F)\le M_2^{\rm NL}\le M_2$; the lower bound rests on a stronger inequality that we obtain for arbitrary Schmidt bases and rank, thus resolving the open problem of finding the maximal lower bound. We emphasize a structural distinction that makes the non-local quantities the physically preferred diagnostics: whereas the full SRE depends on the (non-unique) encoding of the gauge-invariant local Hilbert space into qubits, both the non-local magic and the anti-flatness are invariant under site-local re-encodings and are therefore intrinsic to the state and bipartition. By varying the gauge coupling on lattices up to $6\times 6$ with bond dimension up to $128$, we find that the non-local magic furnishes a sharper and more bond-dimension-friendly probe of the gauge-matter delocalization crossover compared to the full SRE or the gauge-invariant entanglement entropy, retaining a clear signal at bond dimensions well below those needed to converge the ground state itself.

The work was motivated by the numerical result that in a pure SU(2) gauge theory the ratio R of the effective non-compact and compact lattice spacing is larger than 1 and increasing with decreasing gauge coupling, as well as the expectation that it should further increase extending the parameter space. This means that with a noncompact regularization, at given number of lattice sites and comparable scaling, one can obtain a larger physical volume, whose importance for the control of size effects has long been known. We confirm qualitatively results and expectation by a perturbative evaluation of the effective lattice spacing in an expansion in the Plank constant of non-compact pure SU(2) and Abelian gauge theories, but we find in addition that R reaches the maximum value of sqrt(2). Including matter fields we find that R increases ( still up to sqrt(2) ) or decreases depending on the difference between the number of scalar and spinor degrees of freedom, and there are bounds on such a difference.

The signal-to-noise problem limits the reach of many lattice calculations. We present a variational framework that recasts it as a transport problem: the loss of signal reflects a mismatch between the distribution one samples and the one needed to measure an observable, and can be reduced by transporting configurations to close that gap. The optimal transport is typically determined either through a stochastic estimator based on Langevin dynamics or by parametrising it as a normalising flow trained with automatic differentiation. We discuss how the framework brings these methods under a common variational principle and present results for scalar theories.

The two-dimensional Majorana-Hubbard model on the $\pi$-flux lattice involves the most local interaction possible for a lattice with one relativistic Majorana fermion per site. It is predicted to host a Majorana semimetal, dimerized phases, and quantum-critical points with an emergent $U(1)$ symmetry. Nonperturbative lattice calculations for this model remain a major open challenge, thus far limited to zero hopping. We present quantum Monte Carlo simulations of the model at finite hopping using Hamiltonian fermion bags, which are based on a continuous-time expansion with Boltzmann weights that are Pfaffians of a matrix with dimension set by the expansion order, and which give the sign of the weight. Sign problem severity is related to the location of zero modes in the free hopping matrix, and for couplings $g\lesssim 0.7$ and $\beta=L/4$ it is fully removed for lattices up to at least $256$ sites. The interaction strength $g>0$ enhances the $U(1)$-charged dimerization doublet and suppresses the neutral channel, as the renormalization group predicts. Increasing the interactions also restores $U(1)$ symmetry in the component of the dimerization correlator that is even under bond orientation exchange, but not its odd component. There is a persistent anisotropy in the odd component with the symmetry of a lattice nematic. The data is consistent with a gapless semimetal throughout the sign-problem-minimal window.

The dynamics of gauge theories is of fundamental interest, with low-dimensional systems displaying a rich phenomenology beyond the rapid thermalization typical of QCD and non-Abelian theories. In particular, recent quantum simulation experiments have reported robust and unexpected signatures of slow relaxation in generic regimes and at large volumes in one-dimensional U(1) lattice gauge theories (LGTs), whose origin remains poorly understood. Here, we present a framework that provides a unified perspective on such slow dynamics and establishes a new route for exploring subdiffusive fractonic hydrodynamics in Rydberg experiments. The backbone of our theory is an exact analytical mapping from U(1) LGTs with a topological $\theta$ angle to non-local kinetically constrained fermionic models with an emergent linear Stark potential. In the absence of the $\theta$ term, this framework interprets the non-thermal dynamics reported in recent experiments as prethermal behavior arising from proximity to an integrable free-fermion model. For non-zero $\theta$, the emergent Stark potential instead explains the freezing dynamics observed in other recent experiments. We argue that this correspondence could also lead to subdiffusive transport due to emergent conservation laws. We predict that these phenomena arise in a much broader class of models, and support this prediction with numerical simulations and proposals for future experiments.

Relativistic heavy-ion collisions provide a unique experimental opportunity to study strongly interacting matter at extreme temperature and density, while lattice quantum chromodynamics (QCD) offers a first-principles approach to the equilibrium properties of such matter in the non-perturbative regime. The interplay between experiment and lattice QCD has therefore become central to establishing the properties and phase structure of QCD matter. Selected areas where this connection is particularly informative are discussed, including the QCD equation of state and its role in hydrodynamic descriptions of heavy-ion collisions, transport properties of the quark-gluon plasma, conserved-charge fluctuations and their relation to experimental cumulants, and the ongoing search for a critical point in the QCD phase diagram. Particular attention is given to the limitations involved in confronting equilibrium lattice calculations with the finite, dynamical and experimentally constrained systems produced in heavy-ion collisions. Recent developments increasingly allow quantitative tests of QCD thermodynamics over an extended range of temperature and baryon chemical potential. The continuing experimental programmes at RHIC and the LHC, together with future measurements at FAIR, NICA and the Electron-Ion Collider, provide important opportunities for an increasingly close interplay between lattice QCD, phenomenology and experiment.