Page Curves for General Interacting Systems

Abstract

We calculate in detail the Renyi entanglement entropies of cTPQ states as a function of subsystem volume, filling the details of our prior work [Nature Communications 9, 1635 (2018)], where the formulas were first presented. Working in a limit of large total volume, we find universal formulas for the Renyi entanglement entropies in a region where the subsystem volume is comparable to that of the total system. The formulas are applicable to the infinite temperature limit as well as general interacting systems. For example we find that the second Renyi entropy of cTPQ states in terms of subsystem volume is written universally up to two constants, $S_2(\ell )=-\ln K(\beta )+\ell \ln a(\beta )-\ln \left(1+a(\beta {)}^{-L+2\ell }\right)$, where $L$ is the total volume of the system and $a$ and $K$ are two undetermined constants. The uses of the formulas were already presented in our prior work and we mostly concentrate on the theoretical aspect of the formulas themselves. Aside from deriving the formulas for the Renyi Page curves, the expression for the von Neumann Page curve is also derived, which was not presented in our previous work.

arXiv comment29 pages, 3 figures; JHEP preparation

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• Eigenstate capacity and Page curve in fermionic Gaussian states
• Entanglement formation in continuous-variable random quantum networks
• Dequantizing quantum machine learning models using tensor networks
• How much entanglement can be created in a closed system?
• Entanglement in the Quantum Game of Life
• Page curves and typical entanglement in linear optics
• Entanglement dualities in supersymmetry
• Thermal Pure States for Systems with Antiunitary Symmetries and Their Tensor Network Representations
• Non-Abelian entanglement asymmetry in random states
• Product of Random States and Spatial (Half-)Wormholes
• Volume-law entanglement entropy of typical pure quantum states