World line algorithms

Quantum Monte Carlo World Line Algorithms.613... 

The worm algorithm [40] works in an extended configuration space, where in addition to closed world line configurations one open world line fragment (the worm ) is allowed. Formally this is done by adding a source term to the Hamiltonian which for a spin model is... 

In the second part we have given a short introduction and review of modern world line quantum Monte Carlo algorithms for quantum systems, which are free of any time discretization errors. We have highlighted the fact that... 

The general idea of the world-line Monte Carlo algorithm is similar to that of the quantum-to-classical mapping discussed in the last section. The Hamiltonian is split into two or more terms H = ft such that the matrix... 

Inserting complete sets of basis states between the different Hi factors then leads to a similar representation of the partition function and a similar world-line picture as in the world-line Monte Carlo method. Because there is no Trotter decomposition involved, the method is free of time discretization errors from the outset. Early applications of the SSE method employed local updates, but more efficient cluster-type updates have been developed more recently to overcome the critical slowing down. They include the operator-loop update and the previously mentioned directed-loop algorithm. ... 

To provide quantitative predictions about how to detect the superfluid-insulator transition in these experiments, Kashurnikov, Prokofev and Svistunov performed quantum Monte Carlo simulations of the singleparticle density matrix p,y = (I I /). They used the Bose-Hubbard model with harmonic confining potential and carried out world-line Monte Carlo simulations with the continuous-time Worm algorithm. The diagonal elements of the density matrix provide the real-space particle density, and... 

In many real-world applications, the isomorphism wotild be found before all 16 mappings were checked. For the example from Figure 6-3, many algorithms would find the isomorphism at the fourth mapping following the leftmost path in the search tree the bold line in Figure 6-4) ... 

Figure 9 A 6 yr time series of at nine time-series sites around the world. Values derived from the TOPEX algorithm are shown as a blue line, those from W92 as a green line, and those from LM86 as a red line (Glover et al., 2002) (reproduced hy permission of American Geophysical Union from Geophysical Monographs, 2002,...

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