Related papers: Addressing the sign-problem in Euclidean path inte…
Studying phase transitions in interacting quantum field theories generally requires the numerical study of the dynamical system on an N-dimensional lattice, which is, in most cases, computationally quite the challenging task even with…
This paper proposes a numerical method using neural networks to solve the path integral problem in quantum mechanics for arbitrary potentials. The method is based on a radial basis function expansion of the interaction term that appears in…
We investigate the Euclidean path integral formulation of QCD at finite baryon density and temperature. We show that the partition function Z can be written as a difference between two sums Z+ and Z-, each of which defines a partition…
The sign problem of finite-density QCD at the zero temperature becomes very severe if the quark chemical potential exceeds half of the pion mass. In order to understand its property, we consider the sign problem of the one-site fermion…
The study of QCD phase diagram is very interesting, but we have never understood it well. This is because we face a problem at finite density in QCD. The problem is called sign problem. It causes a decrease of the calculation accuracy. This…
The usual path integral formulation for scalar particles at finite density involves a sign problem, making numerical simulation impractical. We present alternative methods free of this difficulty. We apply these approaches to phi^4 theory…
We investigate the sign problem in 0+1 dimensional QCD at finite chemical potential by using the path optimization method. The SU(3) link variable is complexified to the SL(3,$\mathbb{C}$) link variable, and the integral path is represented…
This article provides a pedagogical introduction to the Silver Blaze problem. This problem refers to the difficulty of reconciling to perspectives on QCD with a chemical potential. The first is the phenomenological fact that at $T=0$ QCD…
We introduce the feedforward neural network to attack the sign problem via the path optimization method. The variables of integration is complexified and the integration path is optimized in the complexified space by minimizing the cost…
In this paper we describe a new integration method for the groups $U(N)$ and $SU(N)$, for which we verified numerically that it is polynomially exact for $N\le 3$. The method is applied to the example of 1-dimensional QCD with a chemical…
This paper reviews some recent progress on QCD functional integrals at nonzero chemical potentials. One issue discussed is the use of QCD inequalities for this regime. In particular, the positivity of the integrand of particular Euclidean…
Many fascinating systems suffer from a severe (complex action) sign problem preventing us from calculating them with Markov Chain Monte Carlo simulations. One promising method to alleviate the sign problem is the transformation of the…
We analyze a complex scalar field with phi-4 interaction and a chemical potential mu on the lattice. An exact flux representation of the partition sum is used which avoids the complex action problem and based on a generalized worm algorithm…
It is sometimes speculated that the sign problem that afflicts many quantum field theories might be reduced or even eliminated by choosing an alternative domain of integration within a complexified extension of the path integral (in the…
The Monte Carlo evaluation of path integrals is one of a few general purpose methods to approach strongly coupled systems. It is used in all branches of Physics, from QCD/nuclear physics to the correlated electron systems. However, many…
QCD at finite densities of heavy quarks is investigated using the density-of-states method. The phase factor expectation value of the quark determinant is calculated to unprecedented precision as a function of the chemical potential.…
We present an exploratory study of chiral effective theories of nuclei with methods adopted from lattice quantum chromodynamics (QCD). We show that the simulations in the Euclidean path integral approach are feasible and that we can…
In lattice field theory, the interactions of elementary particles can be computed via high-dimensional integrals. Markov-chain Monte Carlo (MCMC) methods based on importance sampling are normally efficient to solve most of these integrals.…
We propose new approach to numerical study of quantum spin systems. Our method is based on a fact that one can use any set of states for the path integral as long as it is complete. We apply our method to one-dimensional quantum spin system…
Quantum field theories (QFTs) at finite densities of matter generically involve complex actions. Standard Monte-Carlo simulations based upon importance sampling, which have been producing quantitative first principle results in particle…