30,657 papers in this slice of arXiv.
Heng-Tong Ding, Swagato Mukherjee, Peter Petreczky +1
We propose a universality-based reconstruction of the QCD chiral crossover line from Lee-Yang edge singularities in the complex baryon chemical potential plane. The framework maps lattice-extracted complex Lee-Yang-zero estimates, treated as proxies for edge singularities, to the universal chiral Lee-Yang edge and thereby determines the μB dependence of both the chiral critical line in the light-quark chiral limit and the pseudo-critical crossover line at physical quark masses. As an illustration, we apply the framework to Lee-Yang-zero estimates recently obtained by the Wuppertal-Budapest collaboration from high-statistics lattice QCD simulations. Without imposing the previously determined small-
Arpan Chatterjee, Marco Frasca, Anish Ghoshal +1
Starting from SU(N) on the lattice, we give a rigorous derivation of the Dyson--Schwinger equations in the continuum limit. We formulate the Dyson--Schwinger identities for the lattice Yang--Mills theory directly in terms of the link variables Uμ(m)∈SU(N), exploiting the invariance of the Haar measure under left group translations. This provides an exact lattice derivation of the corresponding master equation for the Wilson action, expressed through left-invariant Lie derivatives acting on individual links. Because the construction is carried out directly on the compact gauge group, it avoids the ambiguities associated with introducing Lie-algebra valued gauge potentials as primary integration variables at finite lattice spacing. For practical applications, in a second part we then break down the gauge degree of freedom by choosing Feynman gauge. We analyze the continuum-limit form of the resulting lattice identities and derive equations for the one- and two-point connected functions. Under a further simplifying reduction, these equations close to a tractable scalar system. Our results establish a direct bridge between exact lattice identities and the functional equations commonly used in continuum nonperturbative studies of Yang--Mills theory.
Dario van den Berg, Anosh Joseph
Topological twisting provides a powerful framework for constructing lattice formulations of supersymmetric gauge theories. In three dimensions, a twisted version of N=4 super Yang--Mills theory can be discretized so that one nilpotent scalar supersymmetry is preserved exactly at nonzero lattice spacing. The remaining seven supersymmetries are broken by lattice artifacts of O(a), where a is the lattice spacing. An important question is whether these supersymmetries are automatically restored in the continuum limit a→0, or whether fine-tuning of the lattice couplings is required. In this work, we derive the additional twisted supersymmetries by combining discrete R-symmetries of the continuum theory with the action of the scalar supercharge. This construction suggests that restoration of rotational symmetry in the continuum limit implies restoration of R-symmetry, leading to an automatic enhancement to the full N=4 supersymmetry without further tuning. These results may enable nonperturbative lattice studies of three-dimensional supersymmetric gauge theories relevant to string theory and mirror symmetry.
L. Ya. Glozman
Multiple lattice evidences support the existence of a confining but chirally symmetric stringy fluid regime of QCD above the chiral symmetry restoration temperature at T_ch 155 MeV. This regime is characterized by an approximate chiral spin symmetry and its extensions which means that the propagating excitations represent the chirally symmetric quarks connected into color singlets by the chromoelectric string. Clear π,π' peaks above T_ch were extracted on the lattice from the spatial and temporal correlators, which become broader with temperature and disappear roughly at 3Tch. The meson-like excitations above T_ch were studied within the manifestly confining and chirally symmetric model. It has been demonstrated that the chiral symmetry restoration in the confining regime happens because of Pauli blocking of the levels, required for the existence of the quark condensate, by the thermal quark excitation. The same Pauli blocking leads to a huge swelling of the low-spin mesons above T_ch which become infinitely large in the chiral limit. This property should be crucial for the explanation of the high collectivity and a very small mean-free path of the constituents above Tch seen experimentally. Here we demonstrate that the swelling of pions above T_ch is a model-independent effect required by current algebra.
Lode Pollet
We reconstruct the 2PI vertex Γ(k,p;q) from Monte Carlo measurements of the connected two-particle correlator for the two-dimensional single-component φ4 lattice field theory and follow it across the Ising transition. Resolving the vertex in the irreducible representations of the point group C4v, we find that the instability is driven by the A1 (ferromagnetic) channel at zero transfer, whose leading eigenvalue of the symmetrized Bethe--Salpeter kernel approaches unity. Substantial B1 (nematic) and B2 (diagonal nematic) contributions cooperate with A1 across all system sizes, highlighting that the soft sector is multidimensional. In real space, the vertex is short-ranged away from criticality while it develops a power-law tail at the critical point. In the ordered phase, the q=0 eigenvalue collapses because the ferromagnetic weight has condensed into the (one-particle-reducible) order parameter (or collective coordinate for a finite system), although finite-momentum fluctuations persist. By stripping the crossed-channel ladders, we obtain the fully irreducible vertex, which is a local contact -- to a very good approximation. Inserted into the parquet and Schwinger--Dyson equations, this contact reproduces the Monte Carlo self-energy with an accuracy better than one-tenth of a percent. This provides a first-principles benchmark of the dynamical local-vertex approximation (DΓA). Additionally, we demonstrate that in the critical region, the physical solution of the parquet equations behaves as a repulsive fixed point, driven initially by a single order-parameter mode.
Yasuyuki Hatsuda, Kengo Kikuchi
We develop a non-perturbative analytic tensor network formulation of PT-symmetric scalar field theories defined on complex integration contours. Applying this formulation to the two-dimensional PT-symmetric φ4 theory at negative quartic coupling, we derive an explicit analytic expression for the initial tensor and show that its components separate into even and odd sectors according to the parity of the sum of the tensor indices. We further formulate the theory on an alternative complex contour and analytically establish, in arbitrary dimensions, an exact finite-volume relation between the lattice partition function defined on this contour and the real part of the analytic continuation of the Hermitian lattice φ4 partition function to negative quartic coupling.
Hiroki Sukeno, Enrico Rinaldi, Takuya Okuda
Measurement-based quantum simulation (MBQS)---a recently proposed architecture for simulating lattice gauge theories---implements Hamiltonian dynamics by consuming a model-specific entangled resource state with adaptive mid-circuit measurements, rather than by a gate-based circuit. The local constraints in lattice gauge theories are mirrored by the higher-form symmetries of the resource state. Here we report, to our knowledge, the first experimental realization of MBQS of real-time dynamics in the (2+1)-dimensional Z2 gauge theory using the Quantinuum System Model H2 trapped-ion processor. We observe coherent evolution of gauge-invariant observables on 2×2 and 3×3 spatial lattices, consuming virtual three-dimensional cluster states of 200 and 288 resource-state qubits that are generated from instantaneous blocks of 48 and 54 qubits within the 56-qubit register by measurement, reset, and re-entanglement. The measurement record that drives the evolution simultaneously provides one-form-symmetry syndromes at no additional cost, enabling postselection that strongly suppresses observed Gauss-law violations and improves aggregate agreement with ideal Trotterized dynamics. Our results demonstrate that MBQS is a viable, symmetry-aware architecture for simulating lattice field theories on present-day hardware.
N. Er, K. Azizi
We investigate the in-medium properties of the open-charm vector mesons Ds∗ and D∗ in hot and dense nuclear matter within the framework of finite-temperature and finite-density QCD sum rules. The analysis incorporates temperature- and density-dependent quark and gluon condensates together with an in-medium continuum threshold constrained by the light-quark condensate. By solving the resulting QCD sum rules, we determine the in-medium masses and leptonic decay constants of the Ds∗± and D∗± mesons over a broad region of the (T,ρ) plane. Both vector mesons undergo substantial in-medium softening, with their masses and leptonic decay constants decreasing as the baryon density increases. The masses exhibit a non-monotonic dependence on baryon density, whereas the leptonic decay constants decrease monotonically throughout the investigated density range. Increasing temperature generally weakens the density-induced modifications, although baryon density remains the dominant driver of the in-medium evolution. The largest mass shifts occur at intermediate-to-high densities, reaching approximately −413 MeV for the Ds∗− meson and −207 MeV for the D∗− meson, while the leptonic decay constants are reduced by more than 68% in both channels at the highest densities considered. We further investigate the particle--antiparticle splittings of the masses and leptonic decay constants induced by finite baryon density. Finite baryon density lifts the vacuum degeneracy between the charge-conjugate states, while increasing temperature generally suppresses the resulting asymmetries. Although the strange and non-strange channels exhibit similar qualitative behavior, quantitative differences emerge in both the in-medium modifications and the particle--antiparticle splittings. ....
Nora Brambilla, Roberto Bruschini, Abhishek Mohapatra +2
Many quarkoniumlike states have been observed above open-flavor thresholds, but their organization and internal structure remain unsettled. We study the isoscalar hidden-charm and hidden-bottom sectors in Born--Oppenheimer effective field theory (BOEFT), between the spin--isospin averaged S+S and S+P thresholds. At leading order, heavy-quark spin decouples, and the quarkonium static potential mixes through string breaking with the lowest tetraquark/open-flavor BO potentials of the same quantum numbers. These potentials are constrained by QCD symmetries, their short- and long-distance behavior, and lattice-QCD data. The only calibrated parameter is the lowest 1−− adjoint meson mass, fixed from the shallow multiplet associated with the χc1(3872). Using T-matrix, K-matrix, and complex-scaling methods, we determine bound states and resonance poles, their masses, pole widths from the included nonstrange S+S channels, normalized pole couplings, and prescription-dependent quarkonium--open-flavor composition measures. Uncoupled hybrid BOEFT multiplets are included as reference levels. The spectrum exhibits a common heavy-quark-spin-symmetry multiplet organization. Most poles are predominantly quarkonium resonances localized at short distances, with the largest open-flavor components closest to threshold. The same equations also generate shallow, spatially extended, open-flavor-dominated states with molecular long-distance characteristics. Their binding energies, radii, and small quarkonium components are highly sensitive to the adjoint meson mass, whereas the higher spectrum is more stable. Together with the hybrid reference levels, the spectrum provides multiplet assignments for most candidates. States not naturally accommodated point to the need for hidden-strange and S+P tetraquark/open-flavor BO sectors and for hybrid--tetraquark and hybrid--quarkonium mixings.
Pauline Schauerte, Jaime Fabián Nieto Castellanos, Arnold Krechel +2
State-of-the-art solvers for the Dirac equation in Lattice QCD are based on adaptive multigrid methods. These require fine-tuning of many algorithmic parameters to achieve optimal performance. We apply a new multigrid approach to Lattice Field Theory adapted from oil-reservoir simulations: Structured-Multiscale Algebraic Multigrid (SM-AMG). This method builds compact aggregates with overlapping borders to coarsen the grid and yields accurate interpolation. A key advantage is that aggregate size is the primary tunable parameter. For our results, we used SM-AMG in an algebraic approach, called Aggregative-Multiscale AMG (AM-AMG). We benchmark the efficiency of AM-AMG against that of DDαAMG, a successful adaptive multigrid solver which alleviates critical slowing down. The two solvers are compared within the framework of the two-flavor Schwinger model using the Wilson discretization. On fine lattices, the operation count of both methods is similar near the critical point and for large volumes, reflecting a comparable computational cost. However, the number of fine-grid iterations is larger for AM-AMG. On coarse lattices, AM-AMG encounters difficulties to remove the low modes close to the critical mass.
Henry Froland, Dorota M. Grabowska, Sebastian Grieninger +8
The recent success of error detecting codes points toward their potential application to fault-tolerant simulations of nature. In this work, we examine the utility of sparse error detection for simulating lattice gauge theories using quantum computers. In particular, we study the time evolution of the lattice Schwinger model embedded into the Iceberg code family, [[N+2,N,2]], as well as the Hypercube code family, [[2N,N,2]]. The lattice of electrons and positrons in the axial gauge is embedded into a single code block or into multiple code blocks, and this work finds that large codeblocks are advantageous in the absence of connectivity constraints. Noisy classical simulations with realistic near-term error rates, infrequent syndrome measurements and physics-aware postselection are found to improve observable estimation. Under realistic noise rates for near-term quantum computers, this work finds that sparse error detection in quantum simulations has the potential to improve accuracy of observable estimation. Additional rounds of error detection are found to systematically drive errors in observables to the noise floor set by the code. These findings suggest that incorporating minimal implementations of fault tolerance in the near-term will enhance the performance of quantum simulations in nuclear physics and high-energy physics.
Santanu Mondal, Rajan Gupta, Sungwoo Park +5
Results for the isovector momentum fraction, ⟨x⟩u−d, helicity moment, ⟨x⟩Δu−Δd, and the transversity moment, ⟨x⟩δu−δd, of the nucleon are presented using high-statistics data on thirteen NME ensembles of gauge configurations generated by the JLab/W&M/LANL/MIT/Marseille collaborations using 2+1-flavors of dynamical Wilson-clover quarks. The much higher statistics facilitated better control over all systematics compared to our previous lattice calculation. The least controlled systematic---excited-state contamination---is quantified by studying the variation of the results as a function of three estimates of the mass gap of the first excited state, obtained from two- and three-point correlation functions. The final results are obtained using a simultaneous fit to extrapolate in the lattice spacing, a, pion and kaon masses, Mπ and MK, and the finite volume parameter, MπL. The data show no significant finite-volume correction, and some dependence on the lattice spacing and the renormalization factors. The largest systematic uncertainty is due to possible remaining excited states contributions. Our final results, in the MS scheme at 2 GeV, are ⟨x⟩u−d=0.154(10)(9), ⟨x⟩Δu−Δd=0.177(10)(15) and ⟨x⟩δu−δd=0.197(12)(18), where the first error is the overall statistical uncertainty and the second represents the various systematic uncertainties added in quadrature. Results for the momentum fraction and helicity moment are consistent with phenomenological global fit values, while the transversity moment is a prediction.
Barbara Andrade, Declan Millar, Lewis Anderson +5
Gauge invariance is central to modern physics and underpins quantum simulations of lattice gauge theories (LGTs). Existing quantum simulation approaches employ Gauss's law either to energetically suppress gauge-violating processes in analog platforms or to detect and discard gauge-violating outcomes in digital devices. Here we introduce a third paradigm, in which Gauss's law is used to dynamically generate the gauge theory itself from a substantially simpler Hamiltonian. Starting from a readily programmable three-body XXX model, we employ experimentally efficient single-qubit U(1) gauge symmetry-generator terms that induce the dynamics of a U(1) LGT. We implement this approach using 101 qubits on a 156-qubit IBM quantum processor and observe real-time dynamics in quantitative agreement with the target LGT while reducing the entangling-gate depth per Trotter step by a factor of five compared with a direct implementation. Our results establish gauge protection as a resource for Hamiltonian engineering rather than merely symmetry preservation, opening a scalable resource-efficient route towards digital quantum simulations of increasingly complex gauge theories in higher spatial dimensions.
Zhiyao Lu, Shu-Heng Shao
We present a fermionic lattice Hamiltonian that exactly realizes the U(1)L×U(1)R global symmetry and the associated chiral anomalies of a massless Dirac fermion in 1+1 dimensions. The construction couples Villain bosons to a Kitaev chain of Majorana fermions, where the bosonic fields are essential for evading Nielsen-Ninomiya-type no-go theorems. For two copies of our model, we realize the anomaly-free U(1)3450 global symmetry and construct symmetric boundary conditions. We analytically demonstrate symmetric mass generation by mapping the symmetry-preserving six-fermion interactions to fermion bilinear terms using fermionic T-duality. Finally, by gauging general anomaly-free global symmetries, we obtain a broad class of lattice chiral gauge theories. As nontrivial applications, we compute the mass spectra of the lattice Schwinger model and the 3450 gauge theory, finding agreement with the corresponding continuum results.
Takayasu Sekihara, Kei Fujiwara
The HAL QCD method has been one of the powerful tools to extract hadron-hadron interactions directly from lattice QCD simulation data. In this paper, we aim at examining the effectiveness of the HAL QCD method by deriving a formula to calculate quantities in the HAL QCD method, such as the so-called R-correlators and HAL QCD local potentials, from the hadron-hadron scattering amplitudes within effective models. In this framework, we can judge whether the HAL QCD local potential, evaluated in the present formula, reproduces the properties of the original hadron-hadron interaction or not via the scattering amplitude, which is a solution of the Lippmann--Schwinger equation with the original hadron-hadron interaction as an input. In an analysis within a simple model of elastic scattering, we show that, when the original interaction is predominantly local, the HAL QCD local potentials quantitatively reproduce phase shifts of the hadron-hadron scatterings and correctly indicate the existence/absence of the bound state with its binding energy ∼ MeV. Lattice discretization of spacetime modifies the results only slightly. Furthermore, we consider the KˉN potential in a bare to KˉN transition amplitude, which shows singular behavior around the origin in the recent HAL QCD results of the lattice QCD simulation data, and discuss the cause of such singular behavior in the HAL QCD method through our model analysis of the KˉN scattering.
Gustavo Ramirez-Hidalgo
The computation of the action of a matrix function on a vector, f(A)b, is a major computational bottleneck for large, sparse matrices, particularly when unfavorable spectral distributions cause standard Krylov subspace methods to stagnate. In this work, we propose a unified framework for preconditioning f(A)b based on the Cauchy integral representation of the matrix function. By exploiting shift-invariance properties, we decouple the preconditioner evaluation from the Krylov subspace generation. We develop this framework in two distinct directions. First, for rational shift-and-invert preconditioning, we resolve a fundamental trade-off between optimal spectral compression and finite-precision instability. We achieve this by formulating a closed-form extraction stabilized via Double Modified Gram-Schmidt reorthogonalization, which eliminates the formation of spurious phantom poles. Second, we present a matrix-free polynomial approach. To ensure numerical stability, we isolate the continuous numerical quadrature step using a Schur decomposition of the projected Hessenberg matrix. To further stabilize the integration near contour singularities and accelerate overall convergence, we incorporate an exact LR-deflation scheme targeting the critical low modes of the preconditioned operator. We analyze the asymptotic stability and proximity to singularity of these methods, and present numerical experiments demonstrating their efficiency on the 2D Laplacian with f=exp, and a highly ill-conditioned Wilson-Dirac operator from lattice quantum chromodynamics with f=sign, although the framework can be in principle used with any f and it is particularly beneficial when applying f(A)bi with many different vectors bi.
Chen Yang
The QCD trace anomaly is a well-established textbook result in quantum field theory with several prominent features: (1) it arises from the quantum breaking of scale symmetry at ultraviolet (UV) scales, yet is independent of the particular UV regulator used, whether lattice or dimensional regularization; (2) although it is nominally proportional to (O(αs)), it is free of renormalization-scheme ambiguity; and (3) it is free of UV divergences and is therefore scale independent. Unfortunately, these important features have been undermined in the recently introduced reducible-basis renormalization, leading to misunderstandings of anomaly-related nucleon physics, including the origins of nucleon mass and internal forces.
Martha Constantinou, Krzysztof Cichy
Parton distribution functions (PDFs) provide one of the most direct ways to describe the partonic structure of hadrons in QCD. They encode nonperturbative information about quarks, antiquarks, and gluons as functions of the partonic momentum fraction x, and they connect this microscopic structure to experimentally measurable high-energy scattering processes through QCD factorization. This makes PDFs interesting to pursue with lattice QCD, which provides a first-principles formulation of the strong interaction. The challenge is that PDFs are defined through light-cone correlations, while lattice QCD is formulated in Euclidean spacetime. This chapter introduces the theoretical foundations and current status of lattice-QCD calculations of PDFs, with emphasis on modern approaches based on spatially nonlocal matrix elements. We first review the light-cone definitions of quark and gluon PDFs, their Mellin moments, and the connection to QCD factorization. We then explain how large-momentum effective theory, short-distance factorization, and the short-distance operator product expansion make it possible to relate Euclidean lattice observables to light-cone partonic structure. Particular attention is given to the elements that have improved over the last five years: renormalization of Wilson-line operators, perturbative matching, finite-momentum and finite-distance effects, reconstruction of the x dependence, and systematic uncertainties. We summarize selected lattice results for proton quark PDFs, pion and kaon PDFs, gluon PDFs, and twist-3 distributions, highlighting both recent progress and remaining challenges. As will be demonstrated, lattice QCD is moving from proof-of-principle calculations toward systematically improvable determinations that can complement experimental data and global QCD analyses in mapping the partonic structure of hadrons.
S. D. Campos
A precise characterization of the QCD phase transition remains a fundamental open problem, primarily due to the intrinsically non-perturbative nature of the dynamics that govern the breakdown of (approximate) scale invariance in the vicinity of the critical temperature Tc. In this work, we formulate a thermodynamic scaling framework for the QCD enthalpy by deriving a linear Callan-Symanzik-type partial differential equation that governs its scale dependence. By mapping macroscopic observables onto a dimensionless auxiliary field space, we define an anomalous thermal dimension, h(T), which probes the trace anomaly and the deformation of the conformal thermodynamic state-space geometry. This framework is confirmed against first-principles Lattice QCD data from the Wuppertal-Budapest collaboration, successfully capturing the localized "scaling bump" associated with the deconfinement crossover, a feature typically missed by analytical models such as the MIT Bag Model. Comparison with known universality classes shows that the enthalpy-based renormalization group flow is highly sensitive to explicit scale breaking from finite quark masses. These results indicate that h(T) acts as a thermodynamic susceptibility to scale transformations, offering a new link between quantum scale anomalies and the information-geometric curvature of strongly interacting matter.
Oliver Gould, Joonas Hirvonen, Andrey Shkerin +1
We study dynamical effects during nucleation in thermal first-order phase transitions in field theory. Focusing on the classical regime of the decay of a metastable state, we present the general formula for the thermal decay rate including the dynamical prefactor and give a recipe for its systematic evaluation. We describe the physical mechanism which reduces the actual thermal decay rate with respect to the statistical rate obtained in equilibrium theory. We also discuss the thermality conditions ensuring the existence of a steady-state thermal rate, in which case our formula is exact up to exponentially small corrections. We show that it reproduces the known results for the nucleation rate in stochastic mechanics and field theory, and allows us to unify and go beyond them. We illustrate this in real-time numerical simulations of simple field theory models. We observe significant non-perturbative contributions which can dominate the dynamical prefactor in weakly-coupled field theories at moderate exponential suppression of the decay rate. We explore the connection of these non-perturbative effects to oscillons. Notably, our numerical method requires exponentially less computing time than direct simulations of decays and is thus applicable to systems with arbitrarily strong exponential suppression. Finally, we discuss small or poorly thermalized systems when the thermality conditions are violated and the steady-state rate does not exist.