Long-range Ising spins models emerging from frustrated Josephson junctions arrays with topological constraints

Geometrical frustration in correlated systems can give rise to a plethora of ordered states and intriguing phases. Here, we theoretically analyze vertex-sharing frustrated Kagome lattices of Josephson junctions and identify various classical and quantum phases. The frustration is provided by periodically arranged 0- and pi-Josephson junctions. In the frustrated regime, the macroscopic phases are composed of different patterns of vortices/antivortices penetrating each basic element of the Kagome lattice, i.e., a superconducting triangle interrupted by three Josephson junctions. We obtain that numerous topological constraints, related to the flux quantization in any hexagon loop, lead to highly anisotropic and long-range interaction between well separated vortices/antivortices. Considering this interaction and a possibility of macroscopic tunneling between vortex and antivortex in single superconducting triangles, we derive an effective Ising-type spin Hamiltonian with strongly anisotropic long-range interaction. In the classically frustrated regime, we numerically calculate the temperature-dependent spatially averaged spin polarization (m) over bar (T) characterizing the crossover between the ordered and disordered vortex/antivortex states. In the coherent quantum regime, we analyze the lifting of the degeneracy of the ground state and the appearance of the highly entangled states.

Automated summary

This article theoretically analyzes the geometrically frustrated Kagome lattices of Josephson junctions and identifies various classical and quantum phases. The research findings reveal that under the constraint conditions, highly anisotropic and long-range interactions occur between vortices/antivortices, affecting the transition between the ordered and disordered states of the system.