Plaquette-type valence bond solid state in the $J_1$-$J_2$ square-lattice Heisenberg model
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929609906323456 |
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| author | Huang, Jiale Qian, Xiangjian Qin, Mingpu |
| author_facet | Huang, Jiale Qian, Xiangjian Qin, Mingpu |
| contents | We utilize Density Matrix Renormalization Group (DMRG) and Fully Augmented Matrix Product States (FAMPS) methods to investigate the Valence Bond Solid (VBS) phase in the $J_1$-$J_2$ square lattice Heisenberg model. To differentiate between the Columnar Valence Bond Solid (CVBS) and Plaquette Valence Bond Solid (PVBS) phases, we introduce an anisotropy $Δ_y$ in the nearest neighboring coupling in the $y$-direction, aiming at detecting the possible spontaneous rotational symmetry breaking in the VBS phase. In the calculations, we push the bond dimension to as large as $D = 25000$ in FAMPS, simulating systems at a maximum size of $14 \times 14$. With a careful extrapolation of the truncation errors and appropriate finite-size scaling, followed by finite $Δ_y$ scaling analysis of the VBS dimer order parameters, we identify the VBS phase as a PVBS type, meaning there is no spontaneous rotational symmetry breaking in the VBS phase. This study not only resolves the long-standing issue of the characterization of the VBS order in the $J_1$-$J_2$ square lattice Heisenberg model but also highlights the capabilities of FAMPS in the study of two-dimensional quantum many-body systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17417 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Plaquette-type valence bond solid state in the $J_1$-$J_2$ square-lattice Heisenberg model Huang, Jiale Qian, Xiangjian Qin, Mingpu Strongly Correlated Electrons Quantum Physics We utilize Density Matrix Renormalization Group (DMRG) and Fully Augmented Matrix Product States (FAMPS) methods to investigate the Valence Bond Solid (VBS) phase in the $J_1$-$J_2$ square lattice Heisenberg model. To differentiate between the Columnar Valence Bond Solid (CVBS) and Plaquette Valence Bond Solid (PVBS) phases, we introduce an anisotropy $Δ_y$ in the nearest neighboring coupling in the $y$-direction, aiming at detecting the possible spontaneous rotational symmetry breaking in the VBS phase. In the calculations, we push the bond dimension to as large as $D = 25000$ in FAMPS, simulating systems at a maximum size of $14 \times 14$. With a careful extrapolation of the truncation errors and appropriate finite-size scaling, followed by finite $Δ_y$ scaling analysis of the VBS dimer order parameters, we identify the VBS phase as a PVBS type, meaning there is no spontaneous rotational symmetry breaking in the VBS phase. This study not only resolves the long-standing issue of the characterization of the VBS order in the $J_1$-$J_2$ square lattice Heisenberg model but also highlights the capabilities of FAMPS in the study of two-dimensional quantum many-body systems. |
| title | Plaquette-type valence bond solid state in the $J_1$-$J_2$ square-lattice Heisenberg model |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2406.17417 |