Finite-temperature critical behaviors in 2D long-range quantum Heisenberg model

Abstract

The well-known Mermin-Wagner theorem prohibits the existence of finite-temperature spontaneous continuous symmetry breaking phase in systems with short-range (SR) interactions at spatial dimension $D\le 2$. For long-range (LR) interaction with monotonic power-law form ($1/r^{\alpha}$), the theorem further forbids a ferro- or antiferromagnetic order at finite temperature when $\alpha\ge 2D$. However, the situation for $\alpha \in (2,4)$ at $D=2$ is beyond the predicting power of the theorem and the situation is still unclear. Here we address this question by large-scale quantum Monte Carlo (QMC) simulations, accompanied with field theoretical analysis. We find the spontaneous breaking of the $SU(2)$ symmetry for $\alpha \in (2,4)$ in ferromagnetic Heisenberg model with $1/r^{\alpha}$ interaction at $D=2$, and obtain the accurate critical exponents by finite-size analysis for $\alpha<3$ where the system is above the upper critical dimension with Gaussian fixed point and for $3\le\alpha<4$ where the system is below the upper critical dimension with non-Gaussian fixed point. Our results reveal the novel critical behaviors in 2D LR Heisenberg models and will intrigue further experimental studies of quantum materials with LR interaction beyond the realm of the Mermin-Wagner theorem.