Critical behavior of the site diluted quantum anisotropic Heisenberg model in two dimensions

• The influence of the dilution x→TBKTx→TBKT using the Self-Consistent Harmonic Approach (SCHA).
• The influence of the dilution →TBKT→TBKT using Quantum Monte Carlo (QMC).
• The limier of percolation is compared using the two methods. TBKT→0TBKT→0, when x→x→xcxc.

In this work we use the Self Consistent Harmonic Approximation and Quantum Monte Carlo technique to study the Quantum XYXY on a two dimensional square lattice in the presence of nonmagnetic impurities. In particular we discuss how site disorder changes the Berezinskii–Kosterlitz–Thouless transition temperature, TBKTTBKT. This temperature is determined as a function of the nonmagnetic density. Our results are consistent with an anomalous behavior of TBKTTBKT at a concentration close to the site percolation threshold. We interpret the results as due to a competition between the confining of vortices and quantum fluctuations, or due to finite size effects.