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Bulletin of the American Physical Society

Applying connectivity twist averaging to quantum Monte Carlo and real solids

Tina N. Mihm, William Z. Van Benschoten, Sai Kumar Ramadugu, Andreas Grüneis, James J. Shepherd

Published Mar 19, 2021• 0 citations
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We develop and test Quantum Monte Carlo algorithms that use a"twist" or a phase in the wave function for fermions in periodic boundary conditions. For metallic systems, averaging over the twist results in faster convergence to the thermodynamic limit than periodic boundary conditions for properties involving the kinetic energy and has the same computational complexity. We determine exponents for the rate of convergence to the thermodynamic limit for the components of the energy of coulomb systems. We show results with twist averaged variational Monte Carlo on free particles, the Stoner model and the electron gas using Hartree-Fock, Slater-Jastrow, and three-body and backflow wave function. We also discuss the use of twist averaging in the grand canonical ensemble, and numerical methods to accomplish the twist averaging.
We present a loop cluster algorithm Monte Carlo method for calculating the local Z(2) Berry phase of the quantum spin models. The Berry connection, which is given as the inner product of two ground states with different local twist angles, is expressed as a Monte Carlo average on the worldlines with fixed spin configurations at the imaginary-time boundaries. The "complex weight problem" caused by the local twist is solved by adopting the meron cluster algorithm. We present the results of simulation on the antiferromagnetic Heisenberg model on an out-of-phase bond-alternating ladder to demonstrate that our method successfully detects the change in the valence bond pattern at the quantum phase transition point. We also propose that the gauge-fixed local Berry connection can be an effective tool to estimate precisely the quantum critical point.