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Register a new userApplication of Maximum Entropy Method to Lattice Field Theory with a Topological Term
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In Monte Carlo simulation, lattice field theory with a $theta$ term suffers from the sign problem. This problem can be circumvented by Fourier-transforming the topological charge distribution $P(Q)$. Although this strategy works well for small lattice volume, effect of errors of $P(Q)$ becomes serious with increasing volume and prevents one from studying the phase structure. This is called flattening. As an alternative approach, we apply the maximum entropy method (MEM) to the Gaussian $P(Q)$. It is found that the flattening could be much improved by use of the MEM.
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Although numerical simulation in lattice field theory is one of the most effective tools to study non-perturbative properties of field theories, it faces serious obstacles coming from the sign problem in some theories such as finite density QCD and lattice field theory with the $theta$ term. We reconsider this problem from the point of view of the maximum entropy method.
In Monte Carlo simulations of lattice field theory with a $theta$ term, one confronts the complex weight problem, or the sign problem. This is circumvented by performing the Fourier transform of the topological charge distribution $P(Q)$. This procedure, however, causes flattening phenomenon of the free energy $f(theta)$, which makes study of the phase structure unfeasible. In order to treat this problem, we apply the maximum entropy method (MEM) to a Gaussian form of $P(Q)$, which serves as a good example to test whether the MEM can be applied effectively to the $theta$ term. We study the case with flattening as well as that without flattening. In the latter case, the results of the MEM agree with those obtained from the direct application of the Fourier transform. For the former, the MEM gives a smoother $f(theta)$ than that of the Fourier transform. Among various default models investigated, the images which yield the least error do not show flattening, although some others cannot be excluded given the uncertainty related to statistical error.
The coupled cluster method has been applied to the eigenvalue problem lattice Hamiltonian QCD (without quarks) for SU(2) gauge fields in two space dimensions. Using a recently presented new formulation and the truncation prescription of Guo et al. we were able to compute the ground state and the lowest $0^+$-glueball mass up to the sixth order of the coupled cluster expansion. The results show evidence for a ``scaling window (i.e. good convergence and constance of dimensionless quantities) around $beta=4/g^2 approx 3$. A comparison of our results to those of other methods is presented.
A $theta$ term in lattice field theory causes the sign problem in Monte Carlo simulations. This problem can be circumvented by Fourier-transforming the topological charge distribution $P(Q)$. This strategy, however, has a limitation, because errors of $P(Q)$ prevent one from calculating the partition function ${cal Z}(theta)$ properly for large volumes. This is called flattening. As an alternative approach to the Fourier method, we utilize the maximum entropy method (MEM) to calculate ${cal Z}(theta)$. We apply the MEM to Monte Carlo data of the CP$^3$ model. It is found that in the non-flattening case, the result of the MEM agrees with that of the Fourier transform, while in the flattening case, the MEM gives smooth ${cal Z}(theta)$.
We study the mass spectra of excited baryons with the use of the lattice QCD simulations. We focus our attention on the problem of the level ordering between the positive-parity excited state N(1440) (the Roper resonance) and the negative-parity excited state N^*(1535). Nearly perfect parity projection is accomplished by combining the quark propagators with periodic and anti-periodic boundary conditions in the temporal direction. Then we extract the spectral functions from the lattice data by utilizing the maximum entropy method. We observe that the masses of the N and N^* states are close for wide range of the quark masses (M_pi=0.61-1.22 GeV), which is in contrast to the phenomenological prediction of the quark models. The role of the Wilson doublers in the baryonic spectral functions is also studied.
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