A detailed description is provided of a new Worm Algorithm, enabling theaccurate computation of thermodynamic properties of quantum many-body systemsin continuous space, at finite temperature. The algorithm is formulated withinthe general Path Integral Monte Carlo (PIMC) scheme, but also allows one toperform quantum simulations in the grand canonical ensemble, as well as tocompute off-diagonal imaginary-time correlation functions, such as theMatsubara Green function, simultaneously with diagonal observables. Anotherimportant innovation consists of the expansion of the attractive part of thepairwise potential energy into elementary (diagrammatic) contributions, whichare then statistically sampled. This affords a complete microscopic account ofthe long-range part of the potential energy, while keeping the computationalcomplexity of all updates independent of the size of the simulated system. Thecomputational scheme allows for efficient calculations of the superfluidfraction and off-diagonal correlations in space-time, for system sizes whichare orders of magnitude larger than those accessible to conventional PIMC. Wepresent illustrative results for the superfluid transition in bulk liquidhelium-four in two and three dimensions, as well as the calculation of thechemical potential of solid helium-four.
展开▼
