Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1009.2197

QCD at non-zero density and canonical partition functions with Wilson fermions

Andrei Alexandru·Urs Wenger
View original source ↗Read source document ↗Export metadata ↓

Abstract

We present a reduction method for Wilson Dirac fermions with non-zero chemical potential which generates a dimensionally reduced fermion matrix. The size of the reduced fermion matrix is independent of the temporal lattice extent and the dependence on the chemical potential is factored out. As a consequence the reduced matrix allows a simple evaluation of the Wilson fermion determinant for any value of the chemical potential and hence the exact projection to the canonical partition functions.

Explore related subjects

hep-lat

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Andrei Alexandru, Urs Wenger. 2010-09-23. QCD at non-zero density and canonical partition functions with Wilson fermions. https://doi.org/10.1103/physrevd.83.034502

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

KEEP EXPLORING

Related papers

arXiv2026

Using lattice chiral effective theory to study pi-pi scattering

We use lattice field theory to study the finite-volume energy spectrum of the $ππ$ system in $SU(2)$ chiral effective field theory (ChEFT) at leading order in the chiral expansion. \hl{This finite-volume spectrum can be directly related to the (infinite-volume) $ππ$ scattering phase shifts by Lüscher's formula.} We compare our results to the finite-volume spectrum obtained from lattice QCD \hl{by the RBC-UKQCD collaboration}. Our calculation and the lattice QCD calculation are both performed with the physical pion mass and the same \sout{physical volume}\hl{lattice volume (as measured in physical units)}. However, we find significant differences between the two calculations in the isospin $I=0$ channel. In particular, there is a nearly stable $σ$ resonance in our lattice ChEFT calculation, which is absent in the lattice QCD calculation. This likely indicates that ChEFT does not converge well with a naive lattice regularization.

hep-lat↗
arXiv2026

Experiment $\leftrightarrow$ lattice QCD: understanding high-temperature QCD matter

Relativistic heavy-ion collisions provide a unique experimental opportunity to study strongly interacting matter at extreme temperature and density, while lattice quantum chromodynamics (QCD) offers a first-principles approach to the equilibrium properties of such matter in the non-perturbative regime. The interplay between experiment and lattice QCD has therefore become central to establishing the properties and phase structure of QCD matter. Selected areas where this connection is particularly informative are discussed, including the QCD equation of state and its role in hydrodynamic descriptions of heavy-ion collisions, transport properties of the quark-gluon plasma, conserved-charge fluctuations and their relation to experimental cumulants, and the ongoing search for a critical point in the QCD phase diagram. Particular attention is given to the limitations involved in confronting equilibrium lattice calculations with the finite, dynamical and experimentally constrained systems produced in heavy-ion collisions. Recent developments increasingly allow quantitative tests of QCD thermodynamics over an extended range of temperature and baryon chemical potential. The continuing experimental programmes at RHIC and the LHC, together with future measurements at FAIR, NICA and the Electron-Ion Collider, provide important opportunities for an increasingly close interplay between lattice QCD, phenomenology and experiment.

hep-lat↗
arXiv2026

Flowed quark field renormalization in lattice QCD: A Ward-identity approach and its validation using quark bilinears

We present a non-perturbative Ward-identity prescription for determining the flowed quark field renormalization factor $Z_χ$, avoiding the computational difficulties of the conventional ringed prescription. The method is based on vector-current normalization and ratios of flowed and unflowed meson two-point functions. We determine the resulting $\mathring{Z}_χ^{V}(t_f,a)$ on five $2+1$-flavor clover ensembles and validate it in the pseudoscalar, scalar, axial-vector, and tensor channels. Renormalized matrix elements obtained through sequential continuum and zero-flow-time extrapolations agree with independent RI/MOM and RI/SMOM determinations. The finite-lattice-spacing bilinear renormalization factors show differences that decrease toward finer lattices, reflecting the different discretization effects of the renormalization methods. The cross-channel agreement demonstrates the viability of the proposed prescription; together, the method and its systematic validation establish a robust foundation for the non-perturbative renormalization of flowed fermionic operators in future lattice calculations.

hep-lat↗