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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, 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.
Highlights
Entanglement plays a central role in quantum many-body theory
In order to obtain information about the spatial entanglement structure, we study the logarithmic negativity of two disjoint blocks of identical size as a function of their separation d, which can be viewed as the entanglement analog to a conventional quantum correlation function
The logarithmic negativity computed in the ground state of the TFIM is depicted in Fig. 3 for various values of the transverse field h, from top to bottom, and several subsystem sizes
Summary
Entanglement plays a central role in quantum many-body theory Exotic quantum phases such as spin liquids[1,2], topological[3,4], or many-body localized systems[5,6,7,8] find their characterization in their entanglement properties. A major limitation of the entanglement entropy is that it is a valid entanglement measure only for pure states. This is a particular challenge in view of experiments where thermal excitations or other imperfections leading to mixed states are generally unavoidable. Recent works on quantum simulators have demonstrated that entanglement in quantum many-body systems can be accessible in experiments. Recent theoretical works have outlined new approaches for measuring entanglement using unitary n-designs[25,26] or machine learning techniques[27]
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