PIMC works by discretizing the imaginary time path integral into a finite number of time slices. Each slice represents the system at a specific point in imaginary time. The resulting discrete paths are then sampled using Monte Carlo techniques. The key steps include:
Discretizing the imaginary time into N slices. Generating random paths through these slices. Calculating the action for each path. Using the Metropolis algorithm to accept or reject paths based on their action. Averaging over accepted paths to compute observables.
