Monte Carlo solution of the Kondo model

The Kondo model is a paradigmatic quantum impurity problem realized in a wide variety of experimental platforms and central to the study of strongly correlated electrons. We introduce a discrete model that exactly reproduces the multichannel Kondo model and demonstrate that it can be simulated efficiently. Using cluster Monte Carlo algorithms, we completely eliminate critical slowing down, providing direct access to universal crossover functions and transport properties across a broad range of parameters. Remarkably, the same model captures both the weak- and strong-coupling regimes, unifying descriptions traditionally derived in complementary limits and revealing their common origin. Our method naturally accommodates large channel numbers, anisotropy, interacting one-dimensional leads, and channel asymmetry, yielding predictions for transport properties in charge-Kondo devices.