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Lee-Yang theory, based on the study of zeros of the partition function, iswidely regarded as a powerful and complimentary approach to the study ofcritical phenomena and forms a foundational part of the theory of phasetransitions. Its widespread use, however, is complicated by the fact that itrequires introducing complex-valued fields that create an obstacle for manynumerical methods, especially in the quantum case where very limited studiesexist beyond one dimension. Here we present a simple and statistically exactmethod to compute partition function zeros with general complex-valued externalfields in the context of large-scale quantum Monte Carlo simulations. Wedemonstrate the power of this approach by extracting critical exponents fromthe leading Lee-Yang zeros of 2D quantum antiferromagnets with a complexstaggered field, focusing on the Heisenberg bilayer and square-lattice $J$-$Q$models. The method also allows us to introduce a complex field that couples tovalence bond solid order, where we observe extended rings of zeros in the$J$-$Q$ model with purely imaginary staggered and valence bond solid fields.

Lee-Yang zeros at $O(3)$ and deconfined quantum critical points