Worm Algorithm and Diagrammatic Monte Carlo: A New Approach to Continuous-Space Path Integral Monte Carlo Simulations

Abstract

A detailed description is provided of a new Worm Algorithm, enabling the accurate computation of thermodynamic properties of quantum many-body systems in continuous space, at finite temperature. The algorithm is formulated within the general Path Integral Monte Carlo (PIMC) scheme, but also allows one to perform quantum simulations in the grand canonical ensemble, as well as to compute off-diagonal imaginary-time correlation functions, such as the Matsubara Green function, simultaneously with diagonal observables. Another important innovation consists of the expansion of the attractive part of the pairwise potential energy into elementary (diagrammatic) contributions, which are then statistically sampled. This affords a complete microscopic account of the long-range part of the potential energy, while keeping the computational complexity of all updates independent of the size of the simulated system. The computational scheme allows for efficient calculations of the superfluid fraction and off-diagonal correlations in space-time, for system sizes which are orders of magnitude larger than those accessible to conventional PIMC. We present illustrative results for the superfluid transition in bulk liquid helium-four in two and three dimensions, as well as the calculation of the chemical potential of solid helium-four.

17 pages, 13 figures

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• Worm Algorithm for Continuous-space Path Integral Monte Carlo Simulations
• Exact, Complete, and Universal Continuous-Time Worldline Monte Carlo Approach to the Statistics of Discrete Quantum Systems
• Critical behavior of the three-dimensional XY universality class
• Worm algorithms for classical statistical models
• Polaron Problem by Diagrammatic Quantum Monte Carlo
• Superglass Phase of Helium-four
• Ring exchanges and the supersolid phase of 4He
• The fate of vacancy-induced supersolidity in 4He
• Superfluidity and Quantum Melting of para-Hydrogen clusters
• Superfluid--Insulator Transition in Commensurate Disordered Bosonic Systems:Large-Scale Worm-Algorithm Simulations
• Path Integral Ground State with a Fourth-Order Propagator: Application to Condensed Helium

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