World-line Monte Carlo algorithm

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 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... 

Quantum Monte Carlo World Line Algorithms.613... 

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