The quantum $p$-spin renormalization group in the large $N$ limit as a benchmark for functional renormalization group
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916962528919552 |
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| author | Lahoche, Vincent Samary, Dine Ousmane Radpay, Parham |
| author_facet | Lahoche, Vincent Samary, Dine Ousmane Radpay, Parham |
| contents | To gain a deeper understanding of the glassy phase in $p$-spin quantum models, this paper examines the dynamics of the $N$-vector $\bm{x} \in \mathbb{R}^N$ through the framework of renormalization group theory. First, we focus on perturbation theory, which is more suitable than nonperturbative techniques due to the specific temporal non-locality of the model after disorder integration. We compute the one-loop $β$-function and explore the structure of its fixed points. Next, we develop the nonperturbative renormalization group approach based on the standard Wetterich-Morris formalism, using two approximation schemes to address the model's non-locality. We investigate the vertex expansion in the symmetric phase and assess the reliability of the approximations for the fixed-point solutions. Finally, we extend our analysis beyond the symmetric phase by using an expansion around the vacuum of the local potential. Our numerical investigations particularly focus on the cases $p = 2$ and $p=3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17600 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The quantum $p$-spin renormalization group in the large $N$ limit as a benchmark for functional renormalization group Lahoche, Vincent Samary, Dine Ousmane Radpay, Parham Disordered Systems and Neural Networks High Energy Physics - Theory To gain a deeper understanding of the glassy phase in $p$-spin quantum models, this paper examines the dynamics of the $N$-vector $\bm{x} \in \mathbb{R}^N$ through the framework of renormalization group theory. First, we focus on perturbation theory, which is more suitable than nonperturbative techniques due to the specific temporal non-locality of the model after disorder integration. We compute the one-loop $β$-function and explore the structure of its fixed points. Next, we develop the nonperturbative renormalization group approach based on the standard Wetterich-Morris formalism, using two approximation schemes to address the model's non-locality. We investigate the vertex expansion in the symmetric phase and assess the reliability of the approximations for the fixed-point solutions. Finally, we extend our analysis beyond the symmetric phase by using an expansion around the vacuum of the local potential. Our numerical investigations particularly focus on the cases $p = 2$ and $p=3$. |
| title | The quantum $p$-spin renormalization group in the large $N$ limit as a benchmark for functional renormalization group |
| topic | Disordered Systems and Neural Networks High Energy Physics - Theory |
| url | https://arxiv.org/abs/2412.17600 |