Parisi's hypercube, Fock-space frustration and near-AdS$_2$/near-CFT$_1$ holography
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| Format: | Preprint |
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2023
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| author | Berkooz, Micha Jia, Yiyang Silberstein, Navot |
| author_facet | Berkooz, Micha Jia, Yiyang Silberstein, Navot |
| contents | We consider a model of Parisi where a single particle hops on an infinite-dimensional hypercube, under the influence of a uniform but disordered magnetic flux. We reinterpret the hypercube as the Fock-space graph of a many-body Hamiltonian and the flux as a frustration of the return amplitudes in Fock space. We will identify the set of observables that have the same correlation functions as the double-scaled Sachdev-Ye-Kitaev (DS-SYK) model, and hence the hypercube model is an equally good quantum model for near-AdS$_2$/near-CFT$_{1}$ (NAdS$_2$/NCFT$_1$) holography. Unlike the SYK model, the hypercube Hamiltonian is not $p$ local. Instead, the SYK model can be understood as a Fock-space model with similar frustrations. Hence we propose this type of Fock-space frustration as the broader characterization for NAdS$_2$/NCFT$_1$ microscopics, which encompasses the hypercube and the DS-SYK models as two specific examples. We then speculate on the possible origin of such frustrations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_18182 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Parisi's hypercube, Fock-space frustration and near-AdS$_2$/near-CFT$_1$ holography Berkooz, Micha Jia, Yiyang Silberstein, Navot High Energy Physics - Theory Disordered Systems and Neural Networks Statistical Mechanics Strongly Correlated Electrons Chaotic Dynamics We consider a model of Parisi where a single particle hops on an infinite-dimensional hypercube, under the influence of a uniform but disordered magnetic flux. We reinterpret the hypercube as the Fock-space graph of a many-body Hamiltonian and the flux as a frustration of the return amplitudes in Fock space. We will identify the set of observables that have the same correlation functions as the double-scaled Sachdev-Ye-Kitaev (DS-SYK) model, and hence the hypercube model is an equally good quantum model for near-AdS$_2$/near-CFT$_{1}$ (NAdS$_2$/NCFT$_1$) holography. Unlike the SYK model, the hypercube Hamiltonian is not $p$ local. Instead, the SYK model can be understood as a Fock-space model with similar frustrations. Hence we propose this type of Fock-space frustration as the broader characterization for NAdS$_2$/NCFT$_1$ microscopics, which encompasses the hypercube and the DS-SYK models as two specific examples. We then speculate on the possible origin of such frustrations. |
| title | Parisi's hypercube, Fock-space frustration and near-AdS$_2$/near-CFT$_1$ holography |
| topic | High Energy Physics - Theory Disordered Systems and Neural Networks Statistical Mechanics Strongly Correlated Electrons Chaotic Dynamics |
| url | https://arxiv.org/abs/2303.18182 |