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Path-integral Monte Carlo method for the local Z2 Berry phase.

Yuichi Motoyama1, Synge Todo

  • 1Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 19, 2013
PubMed
Summary

We developed a Monte Carlo method using a loop cluster algorithm to calculate the Z(2) Berry phase in quantum spin models. This new approach accurately identifies quantum phase transitions by analyzing changes in valence bond patterns.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Computational Physics

Background:

  • Calculating topological invariants like the Berry phase is crucial for understanding quantum phases of matter.
  • Traditional methods often struggle with the
  • complex weight problem
  • in quantum spin systems.

Purpose of the Study:

  • To introduce a novel Monte Carlo method for computing the local Z(2) Berry phase in quantum spin models.
  • To address the challenges associated with local twists in calculating Berry connections.

Main Methods:

  • Development of a loop cluster algorithm Monte Carlo method.
  • Utilizing a meron cluster algorithm to overcome the
  • complex weight problem
  • arising from local twists.
  • Calculating the Berry connection as a Monte Carlo average on worldlines.

Main Results:

  • The method successfully calculates the local Z(2) Berry phase.
  • Simulations on an antiferromagnetic Heisenberg model demonstrated the detection of valence bond pattern changes at quantum phase transitions.
  • The gauge-fixed local Berry connection proved effective in pinpointing quantum critical points.

Conclusions:

  • The presented Monte Carlo method is a powerful tool for studying quantum phase transitions.
  • The local Berry connection serves as a precise indicator for quantum critical points.
  • This approach offers a viable computational strategy for topological phase characterization.