Fine-grained domain counting and percolation analysis in 2D lattice systems with linked-lists

Abstract

We present a fine-grained approach to identify clusters and perform percolation analysis in a 2D lattice system. In our approach, we develop an algorithm based on the linked-list data structure and the members of a cluster are nodes of a path. This path is mapped to a linked-list. This approach facilitates unique cluster labeling in a lattice with a single scan. We use the algorithm to determine the critical exponent in the quench dynamics from Mott Insulator to superfluid phase of bosons in 2D square optical lattices. The result obtained are consistent with the Kibble-Zurek mechanism. We also employ the algorithm to compute correlation lengths using definitions based on percolation theory. And, use it to identify the quantum critical point of the Bose Glass to superfluid transition in the disordered 2D square optical lattices. In addition, we also compute the critical exponent of the transition.