title: Path-integral Monte Carlo method for the local Z2 Berry phase.
abstract: 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.
authors.affiliation: Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan.
authors.forename: Yuichi
authors.initials: Y
authors.lastname: Motoyama
authors.forename: Synge
authors.initials: S
authors.lastname: Todo
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008956:Models, Chemical; D015233:Models, Statistical; D009010:Monte Carlo Method; D044367:Phase Transition; D011789:Quantum Theory