Energy as an entanglement witness for quantum many-body systems

Dowling, Mark R., Doherty, Andrew C. and Bartlett, Stephen D. (2004) Energy as an entanglement witness for quantum many-body systems. Physical Review A, 70 6: 062113-062127. doi:10.1103/PhysRevA.70.062113

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Author Dowling, Mark R.
Doherty, Andrew C.
Bartlett, Stephen D.
Title Energy as an entanglement witness for quantum many-body systems
Journal name Physical Review A   Check publisher's open access policy
ISSN 1050-2947
Publication date 2004-12-01
Sub-type Article (original research)
DOI 10.1103/PhysRevA.70.062113
Open Access Status File (Publisher version)
Volume 70
Issue 6
Start page 062113
End page 062127
Total pages 15
Editor B Crasemann
Place of publication New York
Publisher American Physical Society
Language eng
Subject C1
780102 Physical sciences
240301 Atomic and Molecular Physics
Abstract We investigate quantum many-body systems where all low-energy states are entangled. As a tool for quantifying such systems, we introduce the concept of the entanglement gap, which is the difference in energy between the ground-state energy and the minimum energy that a separable (unentangled) state may attain. If the energy of the system lies within the entanglement gap, the state of the system is guaranteed to be entangled. We find Hamiltonians that have the largest possible entanglement gap; for a system consisting of two interacting spin-1/2 subsystems, the Heisenberg antiferromagnet is one such example. We also introduce a related concept, the entanglement-gap temperature: the temperature below which the thermal state is certainly entangled, as witnessed by its energy. We give an example of a bipartite Hamiltonian with an arbitrarily high entanglement-gap temperature for fixed total energy range. For bipartite spin lattices we prove a theorem demonstrating that the entanglement gap necessarily decreases as the coordination number is increased. We investigate frustrated lattices and quantum phase transitions as physical phenomena that affect the entanglement gap.
Keyword Optics
Physics, Atomic, Molecular & Chemical
Q-Index Code C1
Additional Notes DOI: 101103/PhysRevA/.70.062113

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Created: Wed, 15 Aug 2007, 14:56:21 EST