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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2409.10606 |
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| _version_ | 1866913667384082432 |
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| author | Hawashin, Bilal Rong, Junchen Scherer, Michael M. |
| author_facet | Hawashin, Bilal Rong, Junchen Scherer, Michael M. |
| contents | Spontaneous symmetry breaking can persist at all temperatures in certain biconical $\mathrm{O}(N)\times \mathbb{Z}_2$ vector models when the underlying field theories are ultraviolet complete. So far, the existence of such theories has been established in fractional dimensions for local but nonunitary models or in 2+1 dimensions but for nonlocal models. Here, we study local models at zero and finite temperature directly in 2+1 dimensions employing functional methods. At zero temperature, we establish that our approach describes the quantum critical behaviour with high accuracy for all $N\geq 2$. We then exhibit the mechanism of discrete symmetry breaking from $\mathrm{O}(N)\times \mathbb{Z}_2\to \mathrm{O}(N)$ for increasing temperature near the biconical critical point when $N$ is finite but large. We calculate the corresponding finite-temperature phase diagram and further show that the Hohenberg-Mermin-Wagner theorem is fully respected within this approach, i.e., symmetry breaking only occurs in the $\mathbb{Z}_2$ sector. Finally, we determine the critical $N$ above which this phenomenon can be observed to be $N_c \approx 15$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10606 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | UV complete local field theory of persistent symmetry breaking in 2+1 dimensions Hawashin, Bilal Rong, Junchen Scherer, Michael M. High Energy Physics - Theory Strongly Correlated Electrons Spontaneous symmetry breaking can persist at all temperatures in certain biconical $\mathrm{O}(N)\times \mathbb{Z}_2$ vector models when the underlying field theories are ultraviolet complete. So far, the existence of such theories has been established in fractional dimensions for local but nonunitary models or in 2+1 dimensions but for nonlocal models. Here, we study local models at zero and finite temperature directly in 2+1 dimensions employing functional methods. At zero temperature, we establish that our approach describes the quantum critical behaviour with high accuracy for all $N\geq 2$. We then exhibit the mechanism of discrete symmetry breaking from $\mathrm{O}(N)\times \mathbb{Z}_2\to \mathrm{O}(N)$ for increasing temperature near the biconical critical point when $N$ is finite but large. We calculate the corresponding finite-temperature phase diagram and further show that the Hohenberg-Mermin-Wagner theorem is fully respected within this approach, i.e., symmetry breaking only occurs in the $\mathbb{Z}_2$ sector. Finally, we determine the critical $N$ above which this phenomenon can be observed to be $N_c \approx 15$. |
| title | UV complete local field theory of persistent symmetry breaking in 2+1 dimensions |
| topic | High Energy Physics - Theory Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2409.10606 |