Worm algorithm

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 Ref. [46] we investigated the intermediate strongly interacting regime with rrf > 1, and we determined the critical interaction strength Tqm for the quantum phase transition between the superfluid and the crystal. In our analysis we used a recently developed PIMC-code based on the Worm algorithm [95], which is an exact Monte... 

Boninsegni, M., Prokof ev, N., and Svistunov, B., Worm algorithm for continuous-space path integral Monte Carlo simulations, Phys. Rev. Lett., 96, 070601, 2006. 

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... 

This approach was generalized and improved by adaptation of directed updates [28], to reduce the correlation time in path sampling, and a worm algorithm to sample expectation values of off-diagonal observables [29], In addition, a strategy was introduced to improve upon the fixed-node approximation see Sect. 18.4. Applications included the one-dimensional Heisenberg model and the fermionic Hubbard model. 

Worm and Directed Loop Updates The Loop Algorithm in a Magnetic Field... 

The loop, worm and directed loop algorithms can be used for the simulation of a wide class of quantum magnets. They are of interest not only to theoretical physicists, but also to experimentalists who want to fit experimental measurements to theoretical models. The wide applicability of these methods has led to the publication of open-source versions of these algorithms as part of the ALPS project (Algorithms and Libraries for Physics Simulations) [10] on the web page http //alps.comp-phys.org/. 

The worm and directed loop algorithms are applied when magnetic fields are present. Typical examples include the calculation of magnetization curves of quantum magnets [74], the determination of the first order nature of the spin flop transition in two dimensions [75] and the calculation of phase diagrams of dimerized quantum magnets in a magnetic field [76]. 

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