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arXiv · 1412.3534

Entanglement and the Sign Structure of Quantum States

Tarun Grover·Matthew P. A. Fisher
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Abstract

Many body quantum eigenstates of generic Hamiltonians at finite energy density typically satisfy "volume law" of entanglement entropy: the von Neumann entanglement entropy and the Renyi entropies for a subregion scale in proportion to its volume. Here we provide a connection between the volume law and the sign structure of eigenstates. In particular, we ask the question: can a positive wavefunction support a volume law entanglement? Remarkably, we find that a typical random positive wavefunction, exhibits a constant law for Renyi entanglement entropies $S_n$ for $n>1$, despite arbitrary large amplitude fluctuations. We also provide evidence that the modulus of the finite energy density eigenstates of generic local Hamiltonians show similar behavior.

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Tarun Grover, Matthew P. A. Fisher. 2014-12-11. Entanglement and the Sign Structure of Quantum States. https://doi.org/10.1103/physreva.92.042308

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