Quantum Entanglement and Spectral Form Factor
arXiv:2007.00855
Abstract
We replace a Hamiltonian with a modular Hamiltonian in the spectral form factor and the level spacing distribution function. This study establishes a connection between quantities within Quantum Entanglement and Quantum Chaos. To have a universal study for Quantum Entanglement, we consider the Gaussian random 2-qubit model. The maximum violation of Bell's inequality demonstrates a positive correlation with the entanglement entropy. Thus, the violation plays an equivalent role as Quantum Entanglement. We first provide an analytical estimation of the relation between quantum entanglement quantities and the dip when a subregion only has one qubit. The time of the first dip is monotone for entanglement entropy. The dynamics in a subregion is independent of the initial state at a late time. It is one of the signaling conditions for classical chaos. We also extend our analysis to the Gaussian random 3-qubit state, and it indicates a similar result. The simulation shows that the level spacing distribution function approaches GUE at a late time. In the end, we develop a technique within QFT to the spectral form factor for its relation to an -sheet manifold. We apply the technology to a single interval in CFT and the spherical entangling surface in super Yang-Mills theory. The result is one for both cases, but the Rényi entropy can depend on the Rényi index. For the case of CFT, it indicates the difference between the continuum and discrete spectrum.
arXiv comment21 pages, 8 figures, minor changes
References in corpus (21)
- Mixed State Entanglement and Quantum Error Correction
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Entanglement Entropy and Quantum Field Theory
- A bound on chaos
- Comments on the Sachdev-Ye-Kitaev model
- Black holes and the butterfly effect
- Chaos in AdS holography
- Notes on Some Entanglement Properties of Quantum Field Theory
- Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
- Semiclassical Foundation of Universality in Quantum Chaos
- Bell inequality, Bell states and maximally entangled states for n qubits
- Analytical Spectral Density of the Sachdev-Ye-Kitaev Model at finite N
- Bounding the Space of Holographic CFTs with Chaos
- Entanglement entropy for the n-sphere
- Modular Hamiltonians on the null plane and the Markov property of the vacuum state
- 2D CFT Partition Functions at Late Times
- Universal Spectral Correlations in the Chaotic Wave Function, and the Development of Quantum Chaos
- Holographic Order from Modular Chaos
- Randomness and Chaos in Qubit Models
- Bell's Inequality and Entanglement in Qubits
- The Probe of Curvature in the Lorentzian AdS/CFT Correspondence