PaperPanorama

HEP Lattice·hep-lat

Tue·Aug 4, 2026

6 papers—2 primary·4 cross-listed

All6Primary2Cross-lists4
  1. 01

    Arbitrary-Distance Quantum Error Correction with Gauss's Law for Lattice Gauge Theory

    Neel S. Modi🇺🇸 · Lento Nagano🇯🇵 · Masazumi Honda🇯🇵 · Nobuyuki Yoshioka🇯🇵 · Christian W. Bauer🇺🇸

    It has previously been shown by Rajput, Roggero, and Wiebe that Gauss's law constraints can be used to build efficient quantum error-correcting codes (QECCs) that are robust against arbitrary single-qubit errors. In this work, we generalize the construction to be robust against arbitrary -qubit errors, where is any positive integer. This includes a derivation of the optimal Gauss's law code within the considered family by minimizing the number of physical qubits required for a given code distance. Finally, we compare our codes against other efficient QECCs on metrics such as the number of physical qubits, the locality of the encoded Hamiltonian, and the logical error rate in the code capacity setting. Compared to using a domain-agnostic code for every lattice degree of freedom, we find that the Gauss's law code primarily excels at reducing the locality of the encoded Hamiltonian. Moreover, the physical qubit overhead is also reduced for (distance ).

    hep-lathep-thquant-ph0 citations
  2. 02

    Parton distribution functions from lattice QCD

    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 , 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 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.

    hep-lathep-exhep-phhep-th1 citation
  3. 03

    Dynamics of nucleation in thermal phase transitions

    Oliver Gould🇬🇧 · Joonas Hirvonen🇬🇧 · Andrey Shkerin🇨🇦 · Sergey Sibiryakov🇨🇦

    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.

    ↳ hep-thcond-mat.quant-gascond-mat.softhep-lat+10 citations
  4. 04

    Misconceptions About the Physics of the QCD Trace Anomaly from Renormalization in a Reducible Basis

    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 (), 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.

    ↳ hep-phhep-latnucl-th0 citations
  5. 05

    An Integral-Based Framework for Preconditioning

    Gustavo Ramirez-Hidalgo🇩🇪

    The computation of the action of a matrix function on a vector, , 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 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 , and a highly ill-conditioned Wilson-Dirac operator from lattice quantum chromodynamics with , although the framework can be in principle used with any and it is particularly beneficial when applying with many different vectors .

    ↳ math.NAcs.NAhep-lat0 citations
  6. 06

    Model analysis on the effectiveness of the HAL QCD method for hadron-hadron interactions

    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 potential in a bare to 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 scattering.

    ↳ hep-phhep-latnucl-th0 citations

Affiliations

first authorsco-authorsvia INSPIRE