Sign problem and MEM in lattice field theory with the $θ$ term

Details Sign problem and MEM in lattice field theory with the $θ$ term Sign problem and MEM in lattice field theory with the $θ$ term

2006-02-06

arxiv.org/abs/hep-lat/0602009v2

Prog.Theor.Phys. 115 (2006) 931-949

Physics

High Energy Physics

High Energy Physics - Lattice

PTPTEX<ver.09>, 20 pages with 15 figures

Scientific paper

10.1143/PTP.115.931

Lattice field theory with the $\theta$ term suffers from the sign problem. The sign problem appears as flattening of the free energy. As an alternative to the conventional method, the Fourier transform method (FTM), we apply the maximum entropy method (MEM) to Monte Carlo data obtained using the CP$^3$ model with the $\theta$ term. For data without flattening, we obtain the most probable images of the partition function ${\hat{\cal Z}}(\theta)$ with rather small errors. The results are quantitatively close to the result obtained with the FTM. Motivated by this fact, we systematically investigate flattening in terms of the MEM. Obtained images ${\hat{\cal Z}}(\theta)$ are consistent with the FTM for small values of $\theta$, while the behavior of ${\hat{\cal Z}}(\theta)$ depends strongly on the default model for large values of $\theta$. This behavior of ${\hat{\cal Z}}(\theta)$ reflects the flattening phenomenon.

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