In this review we study quantum field theories and conformal field theories with global
symmetries in the limit of large charge for some of the generators of the symmetry group. At …

The successes and limitations of statistical sampling for a sequence of models studied in the
context of lattice QCD are discussed and the need for new methods to deal with finite …

Quantum field theories (QFTs) at finite densities of matter generically involve complex
actions. Standard Monte Carlo simulations based upon importance sampling, which have …

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 …

We construct an efficient Monte Carlo algorithm that overcomes the severe signal-to-noise
ratio problems and helps us to accurately compute the conformal dimensions of large-Q …

Using the example of the two-dimensional (2D) Ising model, we show that in contrast to what
can be done in configuration space, the tensor renormalization group formulation allows one …

We numerically study the spectral properties, the entanglement and the zero-temperature
phase structure at nonvanishing chemical potential of the O (3) nonlinear sigma model …

One reason for the well-known fact that the complex Langevin (CL) method sometimes fails
to converge or converges to the wrong limit has been identified long ago: it is insufficient …

In this review we present the current state-of-the-art on complex Langevin simulations and
their implications for the QCD phase diagram. After a short summary of the complex …