arXiv:2409.07043

Deviations from maximal entanglement for eigenstates of the Sachdev-Ye-Kitaev model

Yichen Huang, Tan, Yi, Norman Y. Yao

Published Sep 11, 2024• 0 citations

Abstract

We consider mid-spectrum eigenstates of the Sachdev-Ye-Kiteav (SYK) model. We prove that for subsystems whose size is a constant fraction of the system size, the entanglement entropy deviates from the maximum entropy by at least a positive constant. This result highlights the difference between the entanglement entropy of mid-spectrum eigenstates of the SYK model and that of random states.

DOI: 10.48550/arxiv.2409.07043

Related papers

Deviation From Maximal Entanglement for Mid-Spectrum Eigenstates of Local Hamiltonians

Yichen Huang

In a spin chain governed by a local Hamiltonian, we consider a microcanonical ensemble in the middle of the energy spectrum and a contiguous subsystem whose length is a constant fraction of the system size. We prove that if the bandwidth of the ensemble is greater than a certain constant, then the average entanglement entropy (between the subsystem and the rest of the system) of eigenstates in the ensemble deviates from the maximum entropy by at least a positive constant. This result highlights the difference between the entanglement entropy of mid-spectrum eigenstates of (chaotic) local Hamiltonians and that of random states. We also prove that the former deviates from the thermodynamic entropy at the same energy by at least a positive constant.

arXiv:2202.01173IEEE Journal on Selected Areas in Information TheoryJan 1, 20241 citation

Eigenstate Entanglement Entropy in Random Quadratic Hamiltonians

Patrycja Łydżba, Marcos Rigol, Lev Vidmar

The eigenstate entanglement entropy is a powerful tool to distinguish integrable from generic quantum-chaotic models. In integrable models, the average eigenstate entanglement entropy (over all Hamiltonian eigenstates) has a volume-law coefficient that generally depends on the subsystem fraction. In contrast, it is maximal (subsystem fraction independent) in quantum-chaotic models. Using random matrix theory for quadratic Hamiltonians, we obtain a closed-form expression for the average eigenstate entanglement entropy as a function of the subsystem fraction. We test it against numerical results for the quadratic Sachdev-Ye-Kitaev model and show that it describes the results for the power-law random banded matrix model (in the delocalized regime). We show that localization in quasimomentum space produces (small) deviations from our analytic predictions.

arXiv:2006.11302Physical Review LettersOct 27, 202082 citations

Eigenstate entanglement in the Sachdev-Ye-Kitaev model

Yichen Huang, Yingfei Gu

We study the entanglement entropy of eigenstates (including the ground state) of the Sachdev-Ye-Kitaev model. We argue for a volume law, whose coefficient can be calculated analytically from the density of states. The coefficient depends on not only the energy density of the eigenstate but also the subsystem size. Very recent numerical results of Liu et al. confirm our analytical results.

arXiv:1709.09160Physical review. D/Physical review. D.Aug 2, 201964 citations

Entanglement entropy and its quench dynamics for pure states of the Sachdev-Ye-Kitaev model

Pengfei Zhang

Abstract Sachdev-Ye-Kitaev (SYK) is a concrete solvable model with non-Fermi liquid behavior and maximal chaos. In this work, we study the entanglement Rényi entropy for the subsystems of the SYK model in the Kourkoulou-Maldacena states. We use the path-integral approach and take the saddle point approximation in the large-N limit. We find a first-order transition exist when tuning the subsystem size for the q = 4 case, while it is absent for the q = 2 case. We further study the entanglement dynamics for such states under the real-time evolution for noninteracting, weakly interacting and strongly interacting SYK(-like) models.

arXiv:2004.05339Journal of High Energy PhysicsJun 23, 202029 citations

Entanglement Dynamics From Random Product States: Deviation From Maximal Entanglement

Yichen Huang

We study the entanglement dynamics of quantum many-body systems and prove the following: (I) For any geometrically local Hamiltonian on a lattice, starting from a random product state the entanglement entropy is bounded away from the maximum entropy at all times with high probability. (II) In a spin-glass model with random all-to-all interactions, starting from any product state the average entanglement entropy is bounded away from the maximum entropy at all times. We also extend these results to any unitary evolution with charge conservation and to the Sachdev-Ye-Kitaev model. Our results highlight the difference between the entanglement generated by (chaotic) Hamiltonian dynamics and that of random states, for the latter is nearly maximal.

arXiv:2102.07584IEEE Transactions on Information TheoryJan 5, 20225 citations

Quantum entanglement in the Sachdev—Ye—Kitaev model and its generalizations

Pengfei Zhang

Entanglement is one of the most important concepts in quantum physics. We review recent progress in understanding the quantum entanglement in many-body systems using large- N solvable models: the Sachdev—Ye—Kitaev (SYK) model and its generalizations. We present the study of entanglement entropy in the original SYK model using three different approaches: the exact diagonalization, the eigenstate thermalization hypothesis, and the path-integral representation. For coupled SYK models, the entanglement entropy shows linear growth and saturation at the thermal value. The saturation is related to replica wormholes in gravity. Finally, we consider the steady-state entanglement entropy of quantum many-body systems under repeated measurements. The traditional symmetry breaking in the enlarged replica space leads to the measurement-induced entanglement phase transition.

arXiv:2203.01513Frontiers of PhysicsApr 26, 202227 citations