On the basis of a Feynman–Kac-type formula involving Poisson stochastic processes, a Monte Carlo algorithm has recently been introduced, which describes exactly the real- or imaginary-time evolution of many-body lattice quantum systems. We extend this algorithm to the exact simulation of time-dependent correlation functions. The techniques generally employed in Monte Carlo simulations to control fluctuations, namely reconfigurations and importance sampling, are adapted to the present algorithm and their validity is rigorously proved. We complete the analysis by several examples for the hard-core boson Hubbard model and for the Heisenberg model.
Exact Monte Carlo time dynamics in many-body lattice quantum systems / Ostilli, M; Presilla, Carlo. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL. - ISSN 0305-4470. - 38:(2005), pp. 405-426. [10.1088/0305-4470/38/2/009]
Exact Monte Carlo time dynamics in many-body lattice quantum systems
PRESILLA, Carlo
2005
Abstract
On the basis of a Feynman–Kac-type formula involving Poisson stochastic processes, a Monte Carlo algorithm has recently been introduced, which describes exactly the real- or imaginary-time evolution of many-body lattice quantum systems. We extend this algorithm to the exact simulation of time-dependent correlation functions. The techniques generally employed in Monte Carlo simulations to control fluctuations, namely reconfigurations and importance sampling, are adapted to the present algorithm and their validity is rigorously proved. We complete the analysis by several examples for the hard-core boson Hubbard model and for the Heisenberg model.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.