Double-scaled bosonic and fermionic embedded ensembles, complex SYK, and the dual Hilbert space
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| Format: | Preprint |
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2026
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| _version_ | 1866909030609321984 |
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| author | Tall, Jarod Tomsovic, Steven |
| author_facet | Tall, Jarod Tomsovic, Steven |
| contents | We derive the density of states and $2$- and $4$-point functions of embedded ensembles for both fermions and bosons in the double-scaled limit. It is shown the models are equivalent to the double-scaled Sachdev-Ye-Kitaev model, expanding the double-scaled universality class to include both fermionic and bosonic systems. The models can be solved by introducing the Wick product of non-commuting Gaussian random variables. We show that deriving the Wick product is sufficient for computing the density of states, and properties of the Wick product can be used to compute $n$-point functions directly in the energy basis. In this context, the Wick product is equivalent to normal ordering of $q$-oscillators, which leads to the duality between moments of double-scaled models and expectation values in the chord Hilbert space. By considering operator probes as a second set of oscillators, we extend the duality to compute $n$-point functions. Embedded ensembles are equivalent to complex SYK at fixed charge, and we show working directly with embedded ensembles streamlines the derivations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_14522 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Double-scaled bosonic and fermionic embedded ensembles, complex SYK, and the dual Hilbert space Tall, Jarod Tomsovic, Steven High Energy Physics - Theory Quantum Physics We derive the density of states and $2$- and $4$-point functions of embedded ensembles for both fermions and bosons in the double-scaled limit. It is shown the models are equivalent to the double-scaled Sachdev-Ye-Kitaev model, expanding the double-scaled universality class to include both fermionic and bosonic systems. The models can be solved by introducing the Wick product of non-commuting Gaussian random variables. We show that deriving the Wick product is sufficient for computing the density of states, and properties of the Wick product can be used to compute $n$-point functions directly in the energy basis. In this context, the Wick product is equivalent to normal ordering of $q$-oscillators, which leads to the duality between moments of double-scaled models and expectation values in the chord Hilbert space. By considering operator probes as a second set of oscillators, we extend the duality to compute $n$-point functions. Embedded ensembles are equivalent to complex SYK at fixed charge, and we show working directly with embedded ensembles streamlines the derivations. |
| title | Double-scaled bosonic and fermionic embedded ensembles, complex SYK, and the dual Hilbert space |
| topic | High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2604.14522 |