Search arXiv⌕ Search

arXiv · hep-lat/0412030

Order of the Chiral and Continuum Limits in Staggered Chiral Perturbation Theory

Abstract

Durr and Hoelbling recently observed that the continuum and chiral limits do not commute in the two dimensional, one flavor, Schwinger model with staggered fermions. I point out that such lack of commutativity can also be seen in four-dimensional staggered chiral perturbation theory (SChPT) in quenched or partially quenched quantities constructed to be particularly sensitive to the chiral limit. Although the physics involved in the SChPT examples is quite different from that in the Schwinger model, neither singularity seems to be connected to the trick of taking the nth root of the fermion determinant to remove unwanted degrees of freedom ("tastes"). Further, I argue that the singularities in SChPT are absent in most commonly-computed quantities in the unquenched (full) QCD case and do not imply any unexpected systematic errors in recent MILC calculations with staggered fermions.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

C. Bernard. 2006-05-29. Order of the Chiral and Continuum Limits in Staggered Chiral Perturbation Theory. https://doi.org/10.1103/physrevd.71.094020

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Efficient Quantum Simulations of Yang-Mills theory with Maximal-tree Gauge

We develop a quantum algorithmic framework for the efficient simulation of Yang--Mills theories, including the $\mathrm{SU}(3)$ gauge theory in Quantum Chromodynamics (QCD). The framework uses maximal-tree gauge in terms of gauge field variables that removes all local gauge redundancies. In the resulting gauge-fixed formulation and digitization in the field-amplitude basis, we show that Hamiltonian time evolution admits an efficient implementation based on quantum singular value transformation (QSVT). We derive upper bounds on the total number of qubits and gate complexity, finding polynomial scaling with the inverse simulation precision $1/\varepsilon_s$, lattice volume $\mathcal{V}$, gauge coupling $g$, and target energy scale $E$. Our results provide a rigorous complexity-theoretic demonstration that non-Abelian Yang--Mills theories can be simulated efficiently on quantum computers, paving the way toward first-principles quantum simulations of non-perturbative QCD dynamics.

hep-lat↗

Accurate Sampling from Diffusion Models

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.

hep-lat↗

Decomposition of the axial-vector current in a finite box

We consider the matrix element of the axial-vector current between two nucleon states in a finite box. Starting from the chiral Lagrangian density with nucleon and Delta-isobar degrees of freedom, we study the finite-volume effects at the one-loop level. We show that the standard decomposition into the axial-vector and pseudoscalar form factor is incomplete in a finite box. We derive expressions for the complete set of in-box form factors at one loop, and demonstrate how to extract the full set from lattice correlation functions. We verify that the axial Ward identity holds in the chiral limit. We derive the one-loop expressions for the pseudoscalar form factor and verify that the in-box axial Ward identity away from the chiral limit is fulfilled also. Selected numerical results are shown for two flavor-SU(2) lattice ensembles. Sizable finite-volume effects are observed, with an important role for the Delta-isobar. We discuss the implications of our results for lattice studies of the axial-vector current. We conclude that full finite-box results are crucial for a precise determination of the form factors.

hep-lat↗