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

Abstract

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 π-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¯(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.

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