The search for a quantum theory of gravity has led to the discovery of quantum many-body systems that are dual to gravitational models with quantum properties. The perhaps most famous of these systems is the Sachdev-Ye-Kitaev (SYK) model. It features maximal scrambling of quantum information, and opens a potential inroad to experimentally investigating aspects of quantum gravity. A scalable laboratory realisation of this model, however, remains outstanding. Here, we propose a feasible implementation of the SYK model in cavity quantum electrodynamics platforms. Through detailed analytical and numerical demonstrations, we show how driving a cloud of fermionic atoms trapped in a multi-mode optical cavity, and subjecting it to a spatially disordered AC-Stark shift retrieves the physics of the SYK model, with random all-to-all interactions and fast scrambling. Our work provides a blueprint for realising the SYK model in a scalable system, with the prospect of studying holographic quantum matter in the laboratory.The search for a quantum theory of gravity has led to the discovery of quantum many-body systems that are dual to gravitational models with quantum properties. The perhaps most famous of these systems is the Sachdev-Ye-Kitaev (SYK) model. It features maximal scrambling of quantum information, and opens a potential inroad to experimentally investigating aspects of quantum gravity. A scalable laboratory realisation of this model, however, remains outstanding. Here, we propose a feasible implementation of the SYK model in cavity quantum electrodynamics platforms. Through detailed analytical and numerical demonstrations, we show how driving a cloud of fermionic atoms trapped in a multi-mode optical cavity, and subjecting it to a spatially disordered AC-Stark shift retrieves the physics of the SYK model, with random all-to-all interactions and fast scrambling. Our work provides a blueprint for realising the SYK model in a scalable system, with the prospect of studying holographic quantum matter in the laboratory.

arXiv:2303.11343Mar 20, 20234 citations

Solvable model for quantum criticality between the Sachdev-Ye-Kitaev liquid and a disordered Fermi liquid

Oguzhan Can, Marcel Franz

We propose a simple solvable variant of the Sachdev-Ye-Kitaev (SYK) model which displays a quantum phase transition from a fast-scrambling non-Fermi liquid to disordered Fermi liquid. Like the canonical SYK model, our variant involves a single species of Majorana fermions connected by all-to-all random four-fermion interactions. The phase transition is driven by a random two-fermion term added to the Hamiltonian whose structure is inspired by proposed solid-state realizations of the SYK model. Analytic expressions for the saddle-point solutions at a large number $N$ of fermions are obtained and show a characteristic scale-invariant ${\ensuremath{\sim}|\ensuremath{\omega}|}^{\ensuremath{-}1/2}$ behavior of the spectral function below the transition which is replaced by a ${\ensuremath{\sim}|\ensuremath{\omega}|}^{\ensuremath{-}1/3}$ singularity exactly at the critical point. These results are confirmed by numerical solutions of the saddle-point equations and discussed in the broader context of the field.We propose a simple solvable variant of the Sachdev-Ye-Kitaev (SYK) model which displays a quantum phase transition from a fast-scrambling non-Fermi liquid to disordered Fermi liquid. Like the canonical SYK model, our variant involves a single species of Majorana fermions connected by all-to-all random four-fermion interactions. The phase transition is driven by a random two-fermion term added to the Hamiltonian whose structure is inspired by proposed solid-state realizations of the SYK model. Analytic expressions for the saddle-point solutions at a large number $N$ of fermions are obtained and show a characteristic scale-invariant ${\ensuremath{\sim}|\ensuremath{\omega}|}^{\ensuremath{-}1/2}$ behavior of the spectral function below the transition which is replaced by a ${\ensuremath{\sim}|\ensuremath{\omega}|}^{\ensuremath{-}1/3}$ singularity exactly at the critical point. These results are confirmed by numerical solutions of the saddle-point equations and discussed in the broader context of the field.

arXiv:1903.00513Physical review. B./Physical review. BJul 17, 201915 citations

Information scrambling and entanglement dynamics of complex Brownian Sachdev-Ye-Kitaev models

Pengfei Zhang

Abstract In this work, we study the information scrambling and the entanglement dynamics in the complex Brownian Sachdev-Ye-Kitaev (cBSYK) models, focusing on their dependence on the charge density n. We first derive the effective theory for scramblons in a single cBSYK model, which gives closed-form expressions for the late-time OTOC and operator size. In particular, the result for OTOC is consistent with numerical observations in [1]. We then study the entanglement dynamics in cBSYK chains. We derive the density dependence of the entanglement velocity for both Rényi entropies and the Von Neumann entropy, with a comparison to the butterfly velocity. We further consider adding repeated measurements and derive the effective theory of the measurement induced transition which shows U(2)L ⊗ U(2)R symmetry for non-interacting models.Abstract In this work, we study the information scrambling and the entanglement dynamics in the complex Brownian Sachdev-Ye-Kitaev (cBSYK) models, focusing on their dependence on the charge density n. We first derive the effective theory for scramblons in a single cBSYK model, which gives closed-form expressions for the late-time OTOC and operator size. In particular, the result for OTOC is consistent with numerical observations in [1]. We then study the entanglement dynamics in cBSYK chains. We derive the density dependence of the entanglement velocity for both Rényi entropies and the Von Neumann entropy, with a comparison to the butterfly velocity. We further consider adding repeated measurements and derive the effective theory of the measurement induced transition which shows U(2)L ⊗ U(2)R symmetry for non-interacting models.

arXiv:2301.03189Journal of High Energy PhysicsApr 24, 202322 citations

Imbalanced coupled Sachdev-Ye-Kitaev model

Sharmistha Sahoo, Rafael Haenel, Timothy H. Hsieh +1 more

Bulletin of the American Physical SocietyMar 18, 20210 citations

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of fermions are obtained and show a characteristic scale-invariant ${\ensuremath{\sim}|\ensuremath{\omega}|}^{\ensuremath{-}1/2}$ behavior of the spectral function below the transition which is replaced by a ${\ensuremath{\sim}|\ensuremath{\omega}|}^{\ensuremath{-}1/3}$ singularity exactly at the critical point. These results are confirmed by numerical solutions of the saddle-point equations and discussed in the broader context of the field.