Can anybody give reference on calculations of <S_i^+ S_j^+> correlator at nearest-neighbor sites in 2D quantum XY model?

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Florian Hebenstreit

You may find the reference Physica A261, 520-533 (1998) by Brower et al. helpful, where the possibility of measuring Green's functions via loop-cluster algorithms is discussed.

http://www.sciencedirect.com/science/article/pii/S0378437198003252

Stam Nicolis

This paper, http://ptp.oxfordjournals.org/content/63/4/1121.full.pdf

by Takada, seems relevant.