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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.05407 |
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| _version_ | 1866911194186514432 |
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| author | Su, Hang Yao, Yuan Furusaki, Akira |
| author_facet | Su, Hang Yao, Yuan Furusaki, Akira |
| contents | We show that the ground-state expectation value of twisting operator is a topological order parameter for $\text{U}(1)$- and $\mathbb{Z}_{N}$-symmetric symmetry-protected topological (SPT) phases in one-dimensional "spin" systems -- it is quantized in the thermodynamic limit and can be used to identify different SPT phases and to diagnose phase transitions among them. We prove that this (non-local) order parameter must take values in $N$-th roots of unity, and its value can be changed by a generalized lattice translation acting as an $N$-ality transformation connecting distinct phases. This result also implies the Lieb-Schultz-Mattis ingappability for SU($N$) spins if we further impose a general translation symmetry. Furthermore, our exact result for the order parameter of SPT phases can predict a large number of LSM ingappabilities by the general lattice translation. We also apply the $N$-ality property to provide an efficient way to construct possible multi-critical phase transitions starting from a single Hamiltonian with a unique gapped ground state. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05407 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exact quantization of topological order parameter in SU($N$) spin models, $N$-ality transformation and ingappabilities Su, Hang Yao, Yuan Furusaki, Akira Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Mathematical Physics We show that the ground-state expectation value of twisting operator is a topological order parameter for $\text{U}(1)$- and $\mathbb{Z}_{N}$-symmetric symmetry-protected topological (SPT) phases in one-dimensional "spin" systems -- it is quantized in the thermodynamic limit and can be used to identify different SPT phases and to diagnose phase transitions among them. We prove that this (non-local) order parameter must take values in $N$-th roots of unity, and its value can be changed by a generalized lattice translation acting as an $N$-ality transformation connecting distinct phases. This result also implies the Lieb-Schultz-Mattis ingappability for SU($N$) spins if we further impose a general translation symmetry. Furthermore, our exact result for the order parameter of SPT phases can predict a large number of LSM ingappabilities by the general lattice translation. We also apply the $N$-ality property to provide an efficient way to construct possible multi-critical phase transitions starting from a single Hamiltonian with a unique gapped ground state. |
| title | Exact quantization of topological order parameter in SU($N$) spin models, $N$-ality transformation and ingappabilities |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2406.05407 |