Conformal Invariance and Multifractality at Anderson Transitions in Arbitrary Dimensions
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910285455949824 |
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| author | Padayasi, Jaychandran Gruzberg, Ilya A. |
| author_facet | Padayasi, Jaychandran Gruzberg, Ilya A. |
| contents | Multifractals arise in various systems across nature whose scaling behavior is characterized by a continuous spectrum of multifractal exponents $Δ_q$. In the context of Anderson transitions, the multifractality of critical wave functions is described by operators $O_q$ with scaling dimensions $Δ_q$ in a field-theory description of the transitions. The operators $O_q$ satisfy the so-called Abelian fusion expressed as a simple operator product expansion. Assuming conformal invariance and Abelian fusion, we use the conformal bootstrap framework to derive a constraint that implies that the multifractal spectrum $Δ_q$ (and its generalized form) must be quadratic in its arguments in any dimension $d \geq 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_07340 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Conformal Invariance and Multifractality at Anderson Transitions in Arbitrary Dimensions Padayasi, Jaychandran Gruzberg, Ilya A. Disordered Systems and Neural Networks High Energy Physics - Theory Multifractals arise in various systems across nature whose scaling behavior is characterized by a continuous spectrum of multifractal exponents $Δ_q$. In the context of Anderson transitions, the multifractality of critical wave functions is described by operators $O_q$ with scaling dimensions $Δ_q$ in a field-theory description of the transitions. The operators $O_q$ satisfy the so-called Abelian fusion expressed as a simple operator product expansion. Assuming conformal invariance and Abelian fusion, we use the conformal bootstrap framework to derive a constraint that implies that the multifractal spectrum $Δ_q$ (and its generalized form) must be quadratic in its arguments in any dimension $d \geq 2$. |
| title | Conformal Invariance and Multifractality at Anderson Transitions in Arbitrary Dimensions |
| topic | Disordered Systems and Neural Networks High Energy Physics - Theory |
| url | https://arxiv.org/abs/2306.07340 |