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

TL;DR

This paper theoretically investigates a frustrated Kagome lattice of Josephson junctions, revealing emergent long-range Ising spin models with topological constraints, and explores classical and quantum phases including vortex-antivortex states.

Contribution

It introduces a novel effective Ising Hamiltonian with long-range interactions derived from topological constraints in Josephson junction arrays.

Findings

Identification of topologically constrained long-range vortex interactions

Numerical analysis of spin polarization crossover with temperature

Quantum analysis showing degeneracy lifting and entangled states

Abstract

Geometrical frustration in correlated systems can give rise to a plethora of novel ordered states and intriguing phases. Here, we analyze theoretically vertex-sharing frustrated Kagome lattice 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 vortex/antivortex 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). Taking into account 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 calculate numerically the temperature-dependent spatially averaged spins polarization, $\overline{m}(T)$, 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.