Entropy linear response theory with non-Markovian bath

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.

Section: Introductionmentioning

confidence: 99%

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

Zhang

2023

“…Note added. When finishing the manuscript, we become aware of a work by Chen in which the Rényi entropy dynamics has been stuided in a similar model by the perturbation theory [43].…”

Section: A Path-integral Representation Of the Rényi Entropymentioning

confidence: 99%

Page curve from non-Markovianity

Zhang

Zhai

2021

In this paper, we use the exactly solvable Sachdev-Ye-Kitaev model to address the issue of entropy dynamics when an interacting quantum system is coupled to a non-Markovian environment. We find that at the initial stage, the entropy always increases linearly matching the Markovian result. When the system thermalizes with the environment at a sufficiently long time, if the environment temperature is low and the coupling between system and environment is weak, then the total thermal entropy is low and the entanglement between system and environment is also weak, which yields a small system entropy in the long-time steady state. This manifestation of non-Markovian effects of the environment forces the entropy to decrease in the later stage, which yields the Page curve for the entropy dynamics. We argue that this physical scenario revealed by the exact solution of the Sachdev-Ye-Kitaev model is universally applicable for general chaotic quantum many-body systems and can be verified experimentally in near future.

“…Consequently, there is a growing interest in developing entropy response theory for general quantum systems, with the potential for analytical solutions. Pioneering works in this direction include [30,31]. In particular, in [30], the authors investigate the impact of an external impulse on the entropy of open systems prepared in the thermal ensemble.…”

Section: Introductionmentioning

confidence: 99%

Perturbative Page curve induced by external impulse

Zhang

2023

In this work, we extend the recent study of entropy dynamics induced by an external impulse in open quantum systems, where the entropy response follows the Page curve. For small system-bath coupling κ, we expect that the entropy first increases exponentially κ2eϰt in the early-time regime t ≲ |log κ| due to quantum many-body chaos, and then decreases as e−λ0t with λ0 ∝ κ2 due to the energy relaxation. These results are confirmed through explicit calculations using two methods: (1) generalized Boltzmann equation for systems with quasi-particles; (2) scramblon effective theory in the early-time regime and perturbation theory in the late-time regime for 0+1-d systems. We also prove that in the second stage, the entropy of the system is equal to the coarse-grained entropy.