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
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866917689522388992 |
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| author | Liu, Wen-Yuan Poilblanc, Didier Gong, Shou-Shu Chen, Wei-Qiang Gu, Zheng-Cheng |
| author_facet | Liu, Wen-Yuan Poilblanc, Didier Gong, Shou-Shu Chen, Wei-Qiang Gu, Zheng-Cheng |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_13301 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | 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 Liu, Wen-Yuan Poilblanc, Didier Gong, Shou-Shu Chen, Wei-Qiang Gu, Zheng-Cheng Strongly Correlated Electrons Superconductivity 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. |
| title | 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 |
| topic | Strongly Correlated Electrons Superconductivity |
| url | https://arxiv.org/abs/2309.13301 |