Finite-density lattice QCD aims for the first-principle study of QCD at finite density, which
describes the system consisting of many quarks. The main targets are systems such as …

In recent years there has been much progress on the investigation of the QCD phase
diagram with lattice QCD simulations. In this review we focus on the developments in the last …

Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying
quantum field theories, and has led to impressive achievements. In particular, it significantly …

These lecture notes contain an elementary introduction to lattice QCD at nonzero chemical
potential. Topics discussed include chemical potential in the continuum and on the lattice; …

In this review, I recall the nature and the inevitability of the" sign problem" which plagues
attempts to simulate lattice QCD at finite baryon density. I present the main approaches used …

A bstract We consider a hybrid Monte Carlo algorithm which is applicable to lattice theories
defined on Lefschetz thimbles. In the algorithm, any point (field configuration) on a thimble is …

The complex Langevin method is a promising approach to the complex-action problem
based on a fictitious time evolution of complexified dynamical variables under the influence …

The complex Langevin method is a leading candidate for solving the so-called sign problem
occurring in various physical situations. Its most vexing problem is that sometimes it …

We review the theory and applications of complex stochastic quantization to the quantum
many-body problem. Along the way, we present a brief overview of a number of ideas that …

At nonzero chemical potential the numerical sign problem in lattice field theory limits the use
of standard algorithms based on importance sampling. Complex Langevin dynamics …