Abstract:

This talk will present, in a tutorial format, advanced Monte Carlo techniques—such as non-reversible Markov processes and cluster moves—and demonstrate how they can be applied to simulate one-dimensional quantum dissipative systems through their bosonized representation. By reformulating the Hamiltonian as a path integral over a classical scalar field, algorithms originally developed for classical systems can be effectively adapted to tackle quantum problems. The focus will be on the dissipative XXZ spin chain, a model that poses major computational challenges due to critical slowing down, degenerate minima, and long-range interactions. To address these bottlenecks, we introduce an enhanced Event-Chain Monte Carlo (ECMC) algorithm that combines local persistent moves with global cluster updates within an efficient O(1)-complexity framework. Performance analyses demonstrate that this approach outperforms traditional Metropolis algorithms by more than an order of magnitude and remains competitive with state-of-the-art Quantum Monte Carlo methods.