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

TL;DR

This paper introduces a new method to compute Lee-Yang zeros in quantum Monte Carlo simulations, enabling analysis of critical phenomena in 2D quantum antiferromagnets with complex external fields.

Contribution

It presents a statistically exact approach for calculating partition function zeros with complex fields in quantum Monte Carlo, applied to 2D quantum antiferromagnets.

Findings

Extracted critical exponents from Lee-Yang zeros.

Observed rings of zeros with imaginary fields.

Demonstrated method's effectiveness in quantum models.

Abstract

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