Work

Tensor network study of the spin- 1 2 square-lattice J 1 − J 2 − J 3 model: Incommensurate spiral order, mixed valence-bond solids, and multicritical points

Year: 2024

Type: article

Abstract: We use the finite projected entangled pair state (PEPS) method to investigate the global phase diagram of the spin-$\frac{1}{2}$ square-lattice ${J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{3}$ antiferromagnetic (AFM) Heisenberg model. The ground-state phase diagram is established with a rich variety of phases: the N\'eel AFM, gapless quantum spin liquid, valence-bond solid (VBS), stripe AFM, and incommensurate spiral phases. The nature of the VBS region is revealed, which contains a plaquette VBS and a mixed columnar-plaquette VBS, with the emergence of short-range incommensurate spin correlation in some region. The long-range incommensurate magnetic phase is also explicitly characterized as a planar spiral with incommensurate spatial periodicities. Most interestingly, there exist several multicritical points connecting different phases. These findings elucidate the true nature of the long-standing square-lattice ${J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{3}$ antiferromagnet at zero temperature. Our results also pave the way to accurately simulate complex two-dimensional quantum spin systems that may host nonuniform features by means of the finite PEPS.

Source: Physical review. B./Physical review. B

DOI: 10.1103/physrevb.109.235116

Authors: Wen-Yuan Liu, Didier Poilblanc, Shou-Shu Gong, Wei-Qiang Chen, Zheng-Cheng Gu