A sampling of quantum Monte Carlo methods
Michael Lindsey (Courant Institute of Mathematical Sciences, New York University)
In this talk I discuss recent work on Monte Carlo-based approaches to computational quantum physics problems.
In the first part, I consider the problems of computing ground states and excited states of quantum many-body systems, which are eigenpairs of exponentially high-dimensional Hermitian operators. I present a new optimization method within the framework of variational Monte Carlo (VMC). The VMC framework approaches these problems by stochastic optimization over a parametric class of wavefunctions. Of particular interest are recently introduced neural-network-based parametrizations for which this approach yields state-of-the-art results.
In the second part, I consider a lattice system conjectured as a model for high-temperature superconductivity near an antiferromagnetic metallic phase transition. This model can be studied numerically by Monte Carlo methods, but due to cubic computational cost in the lattice volume, previous approaches cannot reach the large-volume limit needed to resolve novel scaling at small momentum. I present recent work toward a linear-scaling approach, which is able to resolve the conjectured non-Hertz-Millis scaling of this model for the first time.