Fine-grained domain counting and percolation analysis in two-dimensional lattice systems with linked lists

Area of Science:

• Condensed Matter Physics
• Quantum Simulation
• Statistical Mechanics

Background:

• Understanding phase transitions in quantum systems is crucial for developing new materials and technologies.
• Percolation theory provides a framework for analyzing connectivity and critical phenomena in disordered systems.
• Bosonic systems in optical lattices offer a controllable platform for studying quantum many-body physics.

Purpose of the Study:

• To introduce a fine-grained algorithm for cluster identification and percolation analysis in 2D lattice systems.
• To apply this algorithm to study quench dynamics and phase transitions in bosonic systems.
• To compute critical exponents and fractal dimensions relevant to quantum criticality.

Main Methods:

• Development of a linked-list-based algorithm for unique cluster labeling in a single scan.
• Application of the algorithm to analyze the Mott insulator to superfluid phase transition in 2D optical lattices.
• Computation of correlation length and critical exponents using percolation theory definitions.

Main Results:

• The algorithm successfully identified clusters and performed percolation analysis in 2D lattice systems.
• Results for critical exponents in quench dynamics are consistent with the Kibble-Zurek mechanism.
• The quantum critical point of the Bose Glass to superfluid transition was identified, and critical exponents and fractal dimensions were computed.

Conclusions:

• The developed algorithm is an effective tool for fine-grained cluster analysis and percolation studies in 2D lattice systems.
• The findings provide insights into quantum phase transitions and critical phenomena in bosonic systems.
• The approach facilitates the computation of key parameters characterizing quantum criticality and system behavior.