Quantum electrodynamics in $2+1$ dimensions (${\mathrm{QED}}_3$) has been proposed as a critical field theory describing the low-energy effective theory of a putative algebraic Dirac spin liquid or of quantum phase transitions in two-dimensional frustrated magnets. We provide compelling evidence that the intricate spectrum of excitations of the elementary but strongly frustrated $J_1\text{−}{J}_2$ Heisenberg model on the triangular lattice is in one-to-one correspondence to a zoo of excitations from ${\mathrm{QED}}_3$, in the quantum spin liquid regime. This evidence includes a large manifold of explicitly constructed monopole and bilinear excitations of ${\mathrm{QED}}_3$, which is thus shown to serve as an organizing principle of phases of matter in triangular lattice antiferromagnets and their low-lying excitations. Moreover, we observe signatures of emergent valence-bond solid (VBS) correlations, which can be interpreted either as evidence of critical VBS fluctuations of an emergent Dirac spin liquid or as a transition from the 120° Néel order to a VBS whose quantum critical point is described by ${\mathrm{QED}}_3$. Our results are obtained by comparing ansatz wave functions from a parton construction to exact eigenstates obtained using large-scale exact diagonalization up to $N=48$ sites.

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作为三角晶格反铁磁体组织原理的2+1维量子电动力学

量子电动力学$2+1$方面 （${\mathrm{量子电动力学}}_3$）已被提出作为临界场论，描述假定的代数狄拉克自旋液体或二维受挫磁体中的量子相变的低能有效理论。我们提供了令人信服的证据，表明基本但强烈受挫的复杂激发光谱$J_1\text{-}{J}_2$三角晶格上的海森堡模型与一系列激励一一对应${\mathrm{量子电动力学}}_3$，在量子自旋液体状态下。该证据包括大量明确构造的单极子和双线性激励${\mathrm{量子电动力学}}_3$因此，这被证明是三角晶格反铁磁体及其低位激发中物质相的组织原理。此外，我们观察到涌现价键固体（VBS）相关性的特征，这可以解释为涌现狄拉克自旋液体的临界 VBS 涨落的证据，也可以解释为从 120° Néel 级到其量子临界点的 VBS 的转变。描述为${\mathrm{量子电动力学}}_3$。我们的结果是通过将部分子构造的 ansatz 波函数与使用大规模精确对角化获得的精确本征态进行比较而获得的$氮=48$网站。