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

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• Lefschetz thimbles decomposition for the Hubbard model on the hexagonal lattice
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• Sea contributions to the electric polarizability of the hadrons
• Lee-Yang zero distribution of high temperature QCD and Roberge-Weiss phase transition
• New approach to canonical partition functions computation in $N_f=2$ lattice QCD at finite baryon density
• Sign problem in finite density lattice QCD
• Probing QCD Phase Structure by Baryon Multiplicity Distribution
• Properties of canonical determinants and a test of fugacity expansion for finite density lattice QCD with Wilson fermions
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• Canonical approach to finite density QCD with multiple precision computation
• Lattice-based QCD equation of state at finite baryon density: Cluster Expansion Model
• Canonical fermion determinants in lattice QCD - Numerical evaluation and properties
• Generalized quark number susceptibilities from fugacity expansion at finite chemical potential for $N_f$ = 2 Wilson fermions
• Net baryon number fluctuations across the chiral phase transition at finite density in the strong coupling lattice QCD
• Schur complement solver for Quantum Monte-Carlo simulations of strongly interacting fermions
• Finite size scaling study of $N_{\text{f}}=4$ finite density QCD on the lattice
• Auxiliary field Monte-Carlo simulation of strong coupling lattice QCD for QCD phase diagram
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• Canonical simulations with worldlines: an exploratory study in ${\varphi }_2^4$ lattice field theory
• Restoring canonical partition functions from imaginary chemical potential
• Canonical simulations of supersymmetric SU(N) Yang-Mills quantum mechanics
• Canonical approach -- Investigation of finite density QCD phase transition
• Low temperature limit of lattice QCD
• Approximating Grassmann valued path integrals with radial basis function neural networks
• A filtering technique for the temporally reduced matrix of the Wilson fermion determinant