Trotter path

Path integral Monte Carlo simulations were performed [175] for the system with Hamiltonian (Eq. (25)) for uj = ujq/J = A (where / = 1) with N = 256 particles and a Trotter dimension P = 64 chosen to achieve good computer performance. It turned out that only data with noise of less than 0.1% led to statistically reliable results, which were only possible to obtain with about 10 MC steps. The whole study took approximately 5000 CPU hours on a CRAY YMP. 

The path-integral formulation of a quantum systems goes back to [37], and forms the basis of most QMC algorithms. Instead of following the historical route and discussing the Trotter-Suzuki (checkerboard) decomposition [38,39] for path integrals with discrete time steps At we will directly describe the continuous-time formulation used in modern codes. 

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