arXiv subjects

Ryan Abbott

Publications and source records attributed to Ryan Abbott.

At least 19 recordsLinked to original sources

arXiv2026

Learning the generating functional for variance reduction in lattice QCD

The generating functional in quantum field theory provides the natural framework for constructing correlation functions as derivatives with respect to source operators. We present a methodology that leverages machine-learned normalizing flows to reduce the variance of arbitrary $N$-point correlation functions of bosonic operators in lattice gauge field theory calculations by encoding a representation of the generating functional. We show that it is possible to systematically approach noiseless estimators of correlation functions in this framework. We demonstrate this methodology with applications to calculations of glueball correlation functions and Wilson loops in Quantum Chromodynamics and Yang-Mills theory. The results show up to three orders of magnitude variance reduction.

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arXiv2026

The Causal Bootstrap: Bounding Smeared Spectral Functions from Non-Perturbative Euclidean Data

This work introduces the causal bootstrap, a framework for bounding smeared spectral observables from finite non-perturbative Euclidean data. The method optimizes over the convex set of positive spectral densities compatible with the data to compute rigorous upper and lower bounds on the target observable. Statistical uncertainties, including correlations, are incorporated through compatibility regions using the covariance matrix. The bounds are equivalent, via Lagrange duality, to certified bounds on the target smearing kernel. For polynomial, rational, and piecewise rational kernels, the resulting dual problems can be reduced to finite-dimensional semidefinite programs using techniques familiar, e.g., in the numerical conformal bootstrap. The present formulation clarifies the relation to moment problems, Nevanlinna--Pick interpolation, and linear kernel-reconstruction methods. Numerical examples demonstrate the method.

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arXiv2026

Variance reduction in lattice QCD observables via normalizing flows

Normalizing flows can be used to construct unbiased, reduced-variance estimators for lattice field theory observables that are defined by a derivative with respect to action parameters. This work implements the approach for observables involving gluonic operator insertions in the SU(3) Yang-Mills theory and two-flavor Quantum Chromodynamics (QCD) in four space-time dimensions. Variance reduction by factors of $10$-$60$ is achieved in glueball correlation functions and in gluonic matrix elements related to hadron structure, with demonstrated computational advantages. The observed variance reduction is found to be approximately independent of the lattice volume, so that volume transfer can be utilized to minimize training costs.

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arXiv2026

Moment Problems and Spectral Functions

Nevanlinna-Pick interpolation and moment problems use the analytic structures provided by causality in order to provide rigorous bounds on smeared spectral functions. This proceedings discusses Nevanlinna-Pick interpolation and moment problems and reviews some useful results, including a simple proof that the space of causal data in Nevanlinna--Pick interpolation is convex.

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arXiv2025

Lattice evidence that scalar glueballs are small

This work reports the first calculation of the gravitational form factors (GFFs) of the scalar glueball, performed via lattice field theory in Yang-Mills theory at a single lattice spacing. The glueball GFFs are compared with those of other hadrons as determined in previous lattice calculations, providing strong indications that glueballs have a different gluonic structure than typical hadronic states. A mass radius of 0.263(31) fm is predicted, supporting previous suggestions that the scalar glueball is significantly smaller than other hadrons. These results point towards a potential smoking-gun characteristic to target by experimental glueball searches.

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arXiv2025

Moment problems and bounds for matrix-valued smeared spectral functions

Numerical analytic continuation arises frequently in lattice field theory, particularly in spectroscopy problems. This work shows the equivalence of common spectroscopic problems to certain classes of moment problems that have been studied thoroughly in the mathematical literature. Mathematical results due to Kovalishina enable rigorous bounds on smeared matrix-valued spectral functions, which are implemented numerically for the first time. The required input is a positive-definite matrix of Euclidean-time correlation functions; such matrices are routinely computed in variational spectrum studies using lattice quantum chromodynamics. This work connects the moment-problem perspective to recent developments using the Rayleigh--Ritz method and Lanczos algorithm. Possible limitations due to finite numerical precision are discussed.

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arXiv2025

Filtered Rayleigh-Ritz is all you need

Recent work has shown that the (block) Lanczos algorithm can be used to extract approximate energy spectra and matrix elements from (matrices of) correlation functions in quantum field theory, and identified exact coincidences between Lanczos analysis methods and others. In this work, we note another coincidence: the Lanczos algorithm is equivalent to the well-known Rayleigh-Ritz method applied to Krylov subspaces. Rayleigh-Ritz provides optimal eigenvalue approximations within subspaces; we find that spurious-state filtering allows these optimality guarantees to be retained in the presence of statistical noise. We explore the relation between Lanczos and Prony's method, their block generalizations, generalized pencil of functions (GPOF), and methods based on the generalized eigenvalue problem (GEVP), and find they all fall into a larger "Prony-Ritz equivalence class", identified as all methods which solve a finite-dimensional spectrum exactly given sufficient correlation function (matrix) data. This equivalence allows simpler and more numerically stable implementations of (block) Lanczos analyses.

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arXiv2025

Progress in Normalizing Flows for 4d Gauge Theories

Normalizing flows have arisen as a tool to accelerate Monte Carlo sampling for lattice field theories. This work reviews recent progress in applying normalizing flows to 4-dimensional nonabelian gauge theories, focusing on two advancements: an architectural improvement referred to as learned active loops, and the application of correlated ensemble methods to QCD with $N_f=2$ dynamical fermions.

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arXiv2024

Gravitational form factors of glueballs in Yang-Mills theory

This work presents preliminary results of the first determination of the energy-momentum tensor form factors of the scalar glueball, referred to as gravitational form factors (GFFs). The calculation has been carried out in lattice Yang-Mills theory at a single lattice spacing. Using variationally optimized operators, the matrix elements are extracted from ratios of three-point functions to two-point functions. The glueball GFFs and their kinematic dependence are compared to those of other hadrons from previous calculations.

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arXiv2024

QCD constraints on isospin-dense matter and the nuclear equation of state

Understanding the behavior of dense hadronic matter is a central goal in nuclear physics as it governs the nature and dynamics of astrophysical objects such as supernovae and neutron stars. Because of the non-perturbative nature of quantum chromodynamics (QCD), little is known rigorously about hadronic matter in these extreme conditions. Here, lattice QCD calculations are used to compute thermodynamic quantities and the equation of state of QCD over a wide range of isospin chemical potentials with controlled systematic uncertainties. Agreement is seen with chiral perturbation theory when the chemical potential is small. Comparison to perturbative QCD at large chemical potential allows for an estimate of the gap in the superconducting phase, and this quantity is seen to agree with perturbative determinations. Since the partition function for an isospin chemical potential, $\mu_I$, bounds the partition function for a baryon chemical potential $\mu_B=3\mu_I/2$, these calculations also provide rigorous non-perturbative QCD bounds on the symmetric nuclear matter equation of state over a wide range of baryon densities for the first time.

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arXiv2024

Practical applications of machine-learned flows on gauge fields

Normalizing flows are machine-learned maps between different lattice theories which can be used as components in exact sampling and inference schemes. Ongoing work yields increasingly expressive flows on gauge fields, but it remains an open question how flows can improve lattice QCD at state-of-the-art scales. We discuss and demonstrate two applications of flows in replica exchange (parallel tempering) sampling, aimed at improving topological mixing, which are viable with iterative improvements upon presently available flows.

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arXiv2024

Multiscale Normalizing Flows for Gauge Theories

Scale separation is an important physical principle that has previously enabled algorithmic advances such as multigrid solvers. Previous work on normalizing flows has been able to utilize scale separation in the context of scalar field theories, but the principle has been largely unexploited in the context of gauge theories. This work gives an overview of a new method for generating gauge fields using hierarchical normalizing flow models. This method builds gauge fields from the outside in, allowing different parts of the model to focus on different scales of the problem. Numerical results are presented for $U(1)$ and $SU(3)$ gauge theories in 2, 3, and 4 spacetime dimensions.

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arXiv2024

Applications of flow models to the generation of correlated lattice QCD ensembles

Machine-learned normalizing flows can be used in the context of lattice quantum field theory to generate statistically correlated ensembles of lattice gauge fields at different action parameters. This work demonstrates how these correlations can be exploited for variance reduction in the computation of observables. Three different proof-of-concept applications are demonstrated using a novel residual flow architecture: continuum limits of gauge theories, the mass dependence of QCD observables, and hadronic matrix elements based on the Feynman-Hellmann approach. In all three cases, it is shown that statistical uncertainties are significantly reduced when machine-learned flows are incorporated as compared with the same calculations performed with uncorrelated ensembles or direct reweighting.

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arXiv2023

Lattice quantum chromodynamics at large isospin density: 6144 pions in a box

We present an algorithm to compute correlation functions for systems with the quantum numbers of many identical mesons from lattice quantum chromodynamics (QCD). The algorithm is numerically stable and allows for the computation of $n$-pion correlation functions for $n \in \{ 1, \dots, N\}$ using a single $N \times N$ matrix decomposition, improving on previous algorithms. We apply the algorithm to calculations of correlation functions with up to 6144 $\pi^+$s using two ensembles of gauge field configurations generated with quark masses corresponding to a pion mass $m_\pi = 170$ MeV and spacetime volumes of $(4.4^3\times 8.8)\ {\rm fm}^4$ and $(5.8^3\times 11.6)\ {\rm fm}^4$. We also discuss statistical techniques for the analysis of such systems, in which the correlation functions vary over many orders of magnitude. In particular, we observe that the many-pion correlation functions are well approximated by log-normal distributions, allowing the extraction of the energies of these systems. Using these energies, the large-isospin-density, zero-baryon-density region of the QCD phase diagram is explored. A peak is observed in the energy density at an isospin chemical potential $\mu_I\sim 1.5 m_\pi$, signalling the transition into a Bose-Einstein condensed phase. The isentropic speed of sound in the medium is seen to exceed the ideal-gas (conformal) limit ($c_s^2\leq 1/3$) over a wide range of chemical potential before falling towards the asymptotic expectation at $\mu_I\sim 15 m_\pi$. These, and other thermodynamic observables, indicate that the isospin chemical potential must be large for the system to be well described by an ideal gas or perturbative QCD.

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arXiv2023

Normalizing flows for lattice gauge theory in arbitrary space-time dimension

Applications of normalizing flows to the sampling of field configurations in lattice gauge theory have so far been explored almost exclusively in two space-time dimensions. We report new algorithmic developments of gauge-equivariant flow architectures facilitating the generalization to higher-dimensional lattice geometries. Specifically, we discuss masked autoregressive transformations with tractable and unbiased Jacobian determinants, a key ingredient for scalable and asymptotically exact flow-based sampling algorithms. For concreteness, results from a proof-of-principle application to SU(3) lattice gauge theory in four space-time dimensions are reported.

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arXiv2022

Aspects of scaling and scalability for flow-based sampling of lattice QCD

Recent applications of machine-learned normalizing flows to sampling in lattice field theory suggest that such methods may be able to mitigate critical slowing down and topological freezing. However, these demonstrations have been at the scale of toy models, and it remains to be determined whether they can be applied to state-of-the-art lattice quantum chromodynamics calculations. Assessing the viability of sampling algorithms for lattice field theory at scale has traditionally been accomplished using simple cost scaling laws, but as we discuss in this work, their utility is limited for flow-based approaches. We conclude that flow-based approaches to sampling are better thought of as a broad family of algorithms with different scaling properties, and that scalability must be assessed experimentally.

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arXiv2022

Sampling QCD field configurations with gauge-equivariant flow models

Machine learning methods based on normalizing flows have been shown to address important challenges, such as critical slowing-down and topological freezing, in the sampling of gauge field configurations in simple lattice field theories. A critical question is whether this success will translate to studies of QCD. This Proceedings presents a status update on advances in this area. In particular, it is illustrated how recently developed algorithmic components may be combined to construct flow-based sampling algorithms for QCD in four dimensions. The prospects and challenges for future use of this approach in at-scale applications are summarized.

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arXiv2022

Gauge-equivariant flow models for sampling in lattice field theories with pseudofermions

This work presents gauge-equivariant architectures for flow-based sampling in fermionic lattice field theories using pseudofermions as stochastic estimators for the fermionic determinant. This is the default approach in state-of-the-art lattice field theory calculations, making this development critical to the practical application of flow models to theories such as QCD. Methods by which flow-based sampling approaches can be improved via standard techniques such as even/odd preconditioning and the Hasenbusch factorization are also outlined. Numerical demonstrations in two-dimensional U(1) and SU(3) gauge theories with $N_f=2$ flavors of fermions are provided.

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