EXACT, COMPLETE, AND UNIVERSAL CONTINUOUS-TIME WORLDLINE MONTE-CARLO APPROACH TO THE STATISTICS OF DISCRETE QUANTUM-SYSTEMS

We show how the worldline quantum Monte Carlo procedure, which usually relies on an artificial time discretization, can be formulated direct ly in continuous time, rendering the scheme exact. For an arbitrary sy stem with discrete Hilbert space, none of the configuration update pro cedures contain small parameters. We find that the most effective upda te strategy involves the motion of worldline discontinuities (both in space and time), i.e., the evaluation of the Green's function. Being b ased on local updates only, our method nevertheless allows one to work with the grand canonical ensemble and nonzero winding numbers, and to calculate any dynamical correlation function as easily as expectation values of, e.g., total energy. The principles found for the update in continuous time generalize to any continuous variables in the space o f discrete virtual transitions, and in principle also make it possible to simulate continuous systems exactly. (C) 1998 American Institute o f Physics. [S1063-7761(98)01508-X].