Emergent Geometric Hamiltonian and Insulator-Superfluid Phase Transitions

TL;DR

This paper proposes that bosonic insulator-superfluid phase transitions are driven by emergent geometric properties of insulating states, linking quantum phase transitions to percolation universality class.

Contribution

It introduces a geometric perspective on phase transitions using an effective Hamiltonian and demonstrates the universality class of these transitions as percolation.

Findings

Phase transitions are driven by emergent geometric properties.

Quantum phase transitions belong to the percolation universality class.

Effective low energy Hamiltonian captures resonating states and transitions.

Abstract

I argue that certain bosonic insulator-superfluid phase transitions as an interaction constant varies are driven by emergent geometric properties of insulating states. The {\em renormalized} chemical potential and distribution of disordered bosons define the geometric aspect of an effective low energy Hamiltonian which I employ to study various resonating states and quantum phase transitions. In a mean field approximation, I also demonstrate that the quantum phase transitions are in the universality class of a percolation problem.