Real-time simulations of quantum spin chains: Density of states and reweighting approaches

We put the density of states (DoS) approach to Monte Carlo (MC) simulations under a stress test by applying it to a physical problem with the worst possible sign problem: the real-time evolution of a nonintegrable quantum spin chain. Benchmarks against numerical exact diagonalization and stochastic reweighting are presented. Both MC methods, the DoS approach and reweighting, allow for simulations of spin chains as long as L = 40, far beyond exact diagonalizability, though only for short evolution times t <= 1. We identify discontinuities of the DoS as one of the key problems in the MC simulations and propose calculating some of the dominant contributions analytically, increasing the precision of our simulations by several orders of magnitude. Even after these improvements, the DoS is found highly nonsmooth, and therefore, the DoS approach cannot outperform reweighting. We prove this implication theoretically and provide numerical evidence, concluding that the DoS approach is not well suited for quantum real-time simulations with discrete degrees of freedom.