Symmetry protected entanglement in random mixed states
- URL: http://arxiv.org/abs/2112.00032v1
- Date: Tue, 30 Nov 2021 19:00:07 GMT
- Title: Symmetry protected entanglement in random mixed states
- Authors: Kasra Hejazi and Hassan Shapourian
- Abstract summary: We study the effect of symmetry on tripartite entanglement properties of typical states in symmetric sectors of Hilbert space.
In particular, we consider Abelian symmetries and derive an explicit expression for the logarithmic entanglement negativity of systems with $mathbbZ_N$ and $U(1)$ symmetry groups.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Symmetry is an important property of quantum mechanical systems which may
dramatically influence their behavior in and out of equilibrium. In this paper,
we study the effect of symmetry on tripartite entanglement properties of
typical states in symmetric sectors of Hilbert space. In particular, we
consider Abelian symmetries and derive an explicit expression for the
logarithmic entanglement negativity of systems with $\mathbb{Z}_N$ and $U(1)$
symmetry groups. To this end, we develop a diagrammatic method to incorporate
partial transpose within the random matrix theory of symmetric states and
formulate a perturbation theory in the inverse of the Hilbert space dimension.
We further present entanglement phase diagrams as the subsystem sizes are
varied and show that there are qualitative differences between systems with and
without symmetries. We also design a quantum circuit to simulate our setup.
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