Lattice simulations of QCD with $μ_B\neq0$ versus phase quenched QCD

K. Splittorff

Home/Archive/arXiv

arXiv · hep-lat/0505001

Lattice simulations of QCD with $μ_B\neq0$ versus phase quenched QCD

K. Splittorff

View original source ↗Read source document ↗Export metadata ↓

Abstract

Previously published lattice results for QCD at $μ_B\neq0$ are compared to analytic predictions for phase quenched QCD. We observe that the strength of the sign problem in QCD is linked directly to the position of the phase transition line for pion condensation in phase quenched QCD and that the number of terms needed in the Taylor expansion approach depends on the strength of the sign problem. Together this emphasizes the physical importance of the sign problem and helps to clarify the range over which the Taylor expansion approach is practically applicable. Finally, we observe that the positions of the endpoint of the first order chiral phase transition in the QCD phase diagram found in two successive computations by Fodor and Katz are both close to the position of the phase transition line for pion condensation in phase quenched QCD.

Explore related subjects

hep-lat

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

K. Splittorff. 2005-05-03. Lattice simulations of QCD with $μ_B\neq0$ versus phase quenched QCD. https://arxiv.org/abs/hep-lat/0505001

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

KEEP EXPLORING

Related papers

arXiv2026

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↗

arXiv2026

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↗

arXiv2026

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↗