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

TL;DR

This paper demonstrates spontaneous symmetry breaking and identifies new critical behaviors in 2D long-range quantum Heisenberg models with power-law interactions, extending understanding beyond the Mermin-Wagner theorem.

Contribution

It provides the first large-scale quantum Monte Carlo simulations and field theoretical analysis showing symmetry breaking in 2D long-range Heisenberg models for certain interaction ranges.

Findings

Spontaneous SU(2) symmetry breaking observed at certain long-range interaction exponents.

Critical exponents determined for different regimes of the power-law decay.

New critical behaviors identified beyond the scope of the Mermin-Wagner theorem.

Abstract

The Mermin-Wagner theorem states that spontaneous continuous symmetry breaking is prohibited in systems with short-range interactions at spatial dimension $D\le 2$. For long-range interactions with a power-law form ($1/r^{\alpha}$), the theorem further forbids ferromagnetic or antiferromagnetic order at finite temperature when $\alpha\ge 2D$. However, the situation for $\alpha \in (2,4)$ at $D=2$ is not covered by the theorem. To address this, we conduct large-scale quantum Monte Carlo simulations and field theoretical analysis. Our findings show spontaneous breaking of $SU(2)$ symmetry in the ferromagnetic Heisenberg model with $1/r^{\alpha}$-form long-range interactions at $D=2$. We determine critical exponents through finite-size analysis for $\alpha<3$ (above the upper critical dimension with Gaussian fixed point) and $3\le\alpha<4$ (below the upper critical dimension with non-Gaussian fixed point). These results reveal new critical behaviors in 2D long-range Heisenberg models, encouraging further experimental studies of quantum materials with long-range interactions beyond the Mermin-Wagner theorem's scope.