Berezinskii-Kosterlitz-Thouless Transition in Josephson Junction Arrays

Abstract

The quantum XY model shows a Berezinskii-Kosterlitz-Thouless (BKT) transition between a phase with quasi long-range order and a disordered one, like the corresponding classical model. The effect of the quantum fluctuations is to weaken the transition and eventually to destroy it. However, in this respect the mechanism of disappearance of the transition is not yet clear. In this work we address the problem of the quenching of the BKT in the quantum XY model in the region of small temperature and high quantum coupling. In particular, we study the phase diagram of a 2D Josephson junction array, that is one of the best experimental realizations of a quantum XY model. A genuine BKT transition is found up to a threshold value g ⋆ of the quantum coupling, beyond which no phase coherence is established. Slightly below g ⋆ the phase stiffness shows a reentrant behavior at lowest temperatures, driven by strong nonlinear

General phase spaces: from discrete variables to rotor and continuum limits

“…4 Another generalization of the Ising model -the quantum Potts (e.g., [69,82,83] Expanding the first cosine in a limit (Ω ≫ g) similar to that in eq. (51) immediately yields a Hamiltonian for an array of coupled Josephson Junctions in the quantum regime -the quantum XY model (e.g., [86,87]). Alternatively, we can take the infinitely dense circle limit (rot2), in which s s s, m m m → θ θ θ, N N N :…”

“…where J x,y,z > 0, Y Y Y = Z Z Z −1 X X X −1 , and Y Y Y M,L = Z Z Z −M X X X −L . In terms of the conjugate variables s, m (18), we have (87) This model has a conserved quantity for each plaquette, (88) where the M, L factors are necessary for to commute with the J y -term. There are also conserved quantities consisting of Weyl operators along any horizontal or 60-degree zig-zag of the lattice, (89a) and rot → cv).…”