Abstract
In the Monte Carlo study of QCD at finite baryon density based upon the phase reweighting method, the pion condensation in the phase-quenched theory and associated zero-mode prevent us from going to the low-temperature high-density region. We propose a method to circumvent them by a simple modification of the density of state method. We first argue that the standard version of the density of state method, which is invented to solve the overlapping problem, is effective only for a certain ‘good’ class of observables. We then modify it so as to solve the overlap problem for ‘bad’ observables as well. While, in the standard version of the density of state method, we usually constrain an observable we are interested in, we fix a different observable in our new method which has a sharp peak at some particular value characterizing the correct vacuum of the target theory. In the finite-density QCD, such an observable is the pion condensate. The average phase becomes vanishingly small as the value of the pion condensate becomes large, hence it is enough to consider configurations with π+ ≃ 0, where the zero mode does not appear. We demonstrate an effectiveness of our method by using a toy model (the chiral random matrix theory) which captures the properties of finite-density QCD qualitatively. We also argue how to apply our method to other theories including finite-density QCD. Although the example we study numerically is based on the phase reweighting method, the same idea can be applied to more general reweighting methods and we show how this idea can be applied to find a possible QCD critical point.
Highlights
By using a real and positive weight which ‘approximates’ the complex weight and take into account the effect of the non-positivity by using so-called reweighting methods
In the Monte Carlo study of QCD at finite baryon density based upon the phase reweighting method, the pion condensation in the phase-quenched theory and associated zero-mode prevent us from going to the low-temperature high-density region
We demonstrate an effectiveness of our method by using a toy model which captures the properties of finite-density QCD qualitatively
Summary
We explain our method using the chiral RMT as a concrete example. 2.1 β = 2 RMT The action of the β = 2 RMT [20, 21] with chemical potential [22] is given by. We explain our method using the chiral RMT as a concrete example. We assign μ1 = μ2 = μ for the full theory (finite baryon chemical potential) and μ1 = +μ, μ2 = −μ for the phase-quenched theory (isospin chemical potential). We call these matrix models as RMTB and RMTI , respectively. C is the charge conjugation matrix satisfying C−1γμC = −(γμ)T , and T stands for the transpose. It is easy to see explicitly that these properties hold in the RMT
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