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We present a variational study of the helicity moduli of an anisotropicquantum three-dimensional (3D) XY-model of YBCO in superconducting state. It isfound that both the ab-plane and the c-axis helicity moduli, which areproportional to the inverse square of the corresponding magnetic fieldpenetration depth, vary with temperature T as T to the fourth power in the zerotemperature limit. Moreover, the c-axis helicity modulus drops with temperaturemuch faster than the ab-plane helicity modulus because of the weaker Josephsoncouplings along the c-axis compared to those along the ab-plane. These findingsare in disagreement with the experiments on high quality samples of YBCO.Comment: 9 pages, 1 figur

Anisotropy in the helicity modulus of a quantum three-dimensionalXYmodel: application to YBCO