Wilson Fermion Determinant in Lattice QCD

Abstract

We present a formula for reducing the rank of Wilson fermions from $4N_c{N}_x{N}_y{N}_z{N}_t$ to $4N_c{N}_x{N}_y{N}_z$ keeping the value of its determinant. We analyse eigenvalues of a reduced matrix and coefficients $C_n$ in the fugacity expansion of the fermion determinant ${\sum }_n{C}_n(\exp (\mu /T){)}^n$, which play an important role in the canonical formulation, using lattice QCD configurations on a $4^4$ lattice. Numerically, $\log |C_n|$ varies as $N_x{N}_y{N}_z$, and goes easily over the standard numerical range; We give a simple cure for that. The phase of $C_n$ correlates with the distribution of the Polyakov loop in the complex plain. These results lay the groundwork for future finite density calculations in lattice QCD.

20 pages, 2 tables, 32 figures

References in corpus (3)

• Finite density QCD with a canonical approach
• QCD at Zero Baryon Density and the Polyakov Loop Paradox
• Winding expansion techniques for lattice QCD with chemical potential

Cited by in corpus (1)

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