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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.15759 |
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| _version_ | 1866911782484836352 |
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| author | Zhang, Xing-Yu Chi, Runze Liu, Yang Wang, Lei |
| author_facet | Zhang, Xing-Yu Chi, Runze Liu, Yang Wang, Lei |
| contents | Understanding the excitation spectrum in two-dimensional quantum many-body systems has long been a challenging task. We present an approach by introducing an excitation ansatz based on an infinite matrix product state (MPS) on a helix structure. With the canonical form of MPS states, we can accurately extract key properties such as energy, degeneracy, spectrum weight, and scaling behavior of low-energy excited states simultaneously. To validate the effectiveness of this method, we begin by applying it to the critical point of the transverse-field Ising model. The extracted scaling exponent of the energy gap closely aligns with the conformal bootstrap results. Subsequently, we apply this approach to the $J_1$-$J_2$ Heisenberg model on a square lattice. We discover that the degeneracy of lowest-energy excitations serves as a reliable metric for distinguishing different phases. The phase boundary identified by our method is consistent with some of the previous findings. The present method provides a promising avenue for studying the excitation spectrum of two-dimensional quantum many-body systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_15759 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | 2D excitation information by MPS method on infinite helixes Zhang, Xing-Yu Chi, Runze Liu, Yang Wang, Lei Strongly Correlated Electrons Understanding the excitation spectrum in two-dimensional quantum many-body systems has long been a challenging task. We present an approach by introducing an excitation ansatz based on an infinite matrix product state (MPS) on a helix structure. With the canonical form of MPS states, we can accurately extract key properties such as energy, degeneracy, spectrum weight, and scaling behavior of low-energy excited states simultaneously. To validate the effectiveness of this method, we begin by applying it to the critical point of the transverse-field Ising model. The extracted scaling exponent of the energy gap closely aligns with the conformal bootstrap results. Subsequently, we apply this approach to the $J_1$-$J_2$ Heisenberg model on a square lattice. We discover that the degeneracy of lowest-energy excitations serves as a reliable metric for distinguishing different phases. The phase boundary identified by our method is consistent with some of the previous findings. The present method provides a promising avenue for studying the excitation spectrum of two-dimensional quantum many-body systems. |
| title | 2D excitation information by MPS method on infinite helixes |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2310.15759 |