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arXiv · 1805.06935

Sharp entanglement thresholds in the logarithmic negativity of disjoint blocks in the transverse-field Ising chain

Younes Javanmard·Daniele Trapin·Soumya Bera·Jens H. Bardarson·Markus Heyl
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Abstract

Entanglement has developed into an essential concept for the characterization of phases and phase transitions in ground states of quantum many-body systems. In this work, we use the logarithmic negativity to study the spatial entanglement structure in the transverse-field Ising chain both in the ground state and at nonzero temperatures. Specifically, we investigate the entanglement between two disjoint blocks as a function of their separation, which can be viewed as the entanglement analog of a spatial correlation function. We find sharp entanglement thresholds at a critical distance beyond which the logarithmic negativity vanishes exactly and thus the two blocks become unentangled, which holds even in the presence of long-ranged quantum correlations, i.e., at the system's quantum critical point. Using Time-Evolving Block Decimation (TEBD), we explore this feature as a function of temperature and size of the two blocks and present a simple model to describe our numerical observations.

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Younes Javanmard, Daniele Trapin, Soumya Bera, Jens H. Bardarson, Markus Heyl. 2018-05-23. Sharp entanglement thresholds in the logarithmic negativity of disjoint blocks in the transverse-field Ising chain. https://doi.org/10.1088/1367-2630%2Faad9ba

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