Ground state properties of charge and magnetically frustrated two--dimensional quantum Josephson--junction arrays

TL;DR

This paper analyzes the ground state phase diagram of a two-dimensional quantum Josephson-junction array considering charge, magnetic flux, and capacitance effects, providing analytical critical parameters beyond mean-field approximations.

Contribution

It derives an effective quantum non-linear sigma-model and calculates the ground-state phase diagram analytically for various fluxes, improving upon previous mean-field results.

Findings

Analytical expressions for critical Josephson energy E_J^{crit} as a function of E_C, charge q_x, and flux f.

Phase diagrams for flux values 0, 1/2, 1/3, 1/4, and 1/6.

Enhanced understanding of quantum phase transitions in Josephson-junction arrays.

Abstract

We study a quantum Hamiltonian that models an two--dimensional array of Josephson junctions with short range Josephson couplings, (given by the Josephson energy E_J and charging energiey E_C due to the small capacitance of the junctions. We include the effects from both the self-C0 and the junction-C1 capacitances in the presence of external magnetic flux f=fi/fi0 as well as uniform background of charges q_{x}. We derive an effective quantum non--linear sigma-model for the array Hamiltonian which enables us a non mean--field treatment of the zero--temperature phase transition scenario. We calculate the ground--state phase diagram, analytically deriving E_J^{crit}(E_C,q_x,f) for several rational fluxes f=0,1/2,1/3,1/4 and 1/6 that improves upon previous theoretical treatments based on mean--field approximations.