Emergent Symmetry in Frustrated Magnets: From Deconfined Quantum Critical Point to Gapless Quantum Spin Liquid

Emergent symmetry is a unique feature of identifying quantum phase transitions beyond the Landau paradigm. Via large-scale tensor network simulations, we study a spatially anisotropic spin-1/2 square-lattice frustrated antiferromagnetic (AFM) model, i.e., the $J_{1x}$-$J_{1y}$-$J_2$ model, which contains anisotropic nearest-neighbour couplings $J_{1x}$ and $J_{1y}$, and next nearest-neighbour coupling $J_2$. For small $J_{1y}/J_{1x}$, by tuning $J_2$, a direct continuous transition between the AFM and valence-bond solid (VBS) phase is observed. With growing $J_{1y}/J_{1x}$, a gapless quantum spin liquid (QSL) phase gradually emerges in between the AFM and VBS phase. We observe an emergent O(4) symmetry along the AFM-VBS transition line, which is consistent with the prediction of the deconfined quantum critical point (DQCP) theory. Most surprisingly, we find that such an emergent O(4) symmetry still holds for the whole QSL-VBS transition line. These findings reveal the intrinsic relationship between QSL and DQCP, which also provide us with a very strong constraint on quantum field theory description of the QSL phase. The phase diagram and critical exponents therein are also of direct relevance to future experiments on frustrated magnets.
Comment: 5+7 pages, 4+11 figures