Energy as an Entanglement Witness for Quantum Many-Body Systems

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dc.creatorDowling, Mark R.
dc.creatorDoherty, Andrew C.
dc.creatorBartlett, Stephen D.
dc.date2004-08-13
dc.date2005-01-04
dc.date.accessioned2026-07-07T06:10:36Z
dc.date.available2026-07-07T06:10:36Z
dc.descriptionWe 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.
dc.description16 pages, 3 figures, published version
dc.identifierhttps://arxiv.org/abs/quant-ph/0408086
dc.identifierhttp://arxiv.org/abs/quant-ph/0408086
dc.identifierPhys. Rev. A 70, 062113 (2004)
dc.identifierdoi:10.1103/PhysRevA.70.062113
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/92297
dc.subjectQuantum Physics
dc.subjectStatistical Mechanics
dc.titleEnergy as an Entanglement Witness for Quantum Many-Body Systems
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