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Tensor network study of the spin-1/2 square-lattice J₁-J₂-J₃ model: incommensurate spiral order, mixed valence-bond solids, and multicritical points

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arxiv 2309.13301 v2 pith:VGV5TNAO submitted 2023-09-23 cond-mat.str-el cond-mat.supr-con

Tensor network study of the spin-1/2 square-lattice J₁-J₂-J₃ model: incommensurate spiral order, mixed valence-bond solids, and multicritical points

Wen-Yuan Liu , Didier Poilblanc , Shou-Shu Gong , Wei-Qiang Chen , Zheng-Cheng Gu This is my paper
classification cond-mat.str-el cond-mat.supr-con
keywords incommensuratephasephasesspiralsquare-latticediagramfinitemixed
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We use the finite projected entangled pair state (PEPS) method to investigate the global phase diagram of the spin-1/2 square-lattice $J_1$-$J_2$-$J_3$ antiferromagnetic (AFM) Heisenberg model. The ground state phase diagram is established with a rich variety of phases: AFM, gapless quantum spin liquid, valence-bond solid (VBS), stripe, and incommensurate spiral phases. The nature of the VBS region is revealed, containing a plaquette VBS and a mixed columnar-plaquette VBS, with the emergence of short-range incommensurate spin correlations in some region. The long-range incommensurate magnetic phase is also explicitly characterized as a planar spiral with incommensurate spatial periodicities. Most interestingly, there exists several multicritical points connecting different phases. These findings elucidate the true nature of the long-standing square-lattice $J_1$-$J_2$-$J_3$ antiferromagnet at zero-temperature. Our results also pave the way to accurately simulate complex two-dimensional quantum systems that may host nonuniform features by means of finite PEPS.

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