Spectral Tensor Networks for Computational Statistical Mechanics

Statistical mechanics links the microscopic physics of many-particle systems to their collective, macroscopic behaviors. Computing the statistics of these systems via sampling with conventional methods, like Monte Carlo and molecular dynamics, requires extensive computational effort. Tensor networks avoid sampling and calculate the statistics directly via large-scale tensor contractions. In this talk, I will show how spectral tensor networks, which are specialized to represent multivariate functions, are a flexible and powerful method to simulate high-dimensional systems. I will highlight our efforts to apply spectral tensor networks to challenging domains — including stochastic classical and quantum dynamics as well as the statistical mechanics of lattice and molecular systems — and to extend their reach beyond quasi-one-dimensional problems.