dorsal/arxiv
View SchemaEnergy as an Entanglement Witness for Quantum Many-Body Systems
| Authors | Mark R. Dowling, Andrew C. Doherty, Stephen D. Bartlett |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0408086 |
| URL | https://arxiv.org/abs/quant-ph/0408086 |
| DOI | 10.1103/PhysRevA.70.062113 |
| Journal | Phys. Rev. A 70, 062113 (2004) |
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.
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"abstract": "We investigate quantum many-body systems where all low-energy states are\nentangled. As a tool for quantifying such systems, we introduce the concept of\nthe entanglement gap, which is the difference in energy between the\nground-state energy and the minimum energy that a separable (unentangled) state\nmay attain. If the energy of the system lies within the entanglement gap, the\nstate of the system is guaranteed to be entangled. We find Hamiltonians that\nhave the largest possible entanglement gap; for a system consisting of two\ninteracting spin-1/2 subsystems, the Heisenberg antiferromagnet is one such\nexample. We also introduce a related concept, the entanglement-gap temperature:\nthe temperature below which the thermal state is certainly entangled, as\nwitnessed by its energy. We give an example of a bipartite Hamiltonian with an\narbitrarily high entanglement-gap temperature for fixed total energy range. For\nbipartite spin lattices we prove a theorem demonstrating that the entanglement\ngap necessarily decreases as the coordination number is increased. We\ninvestigate frustrated lattices and quantum phase transitions as physical\nphenomena that affect the entanglement gap.",
"arxiv_id": "quant-ph/0408086",
"authors": [
"Mark R. Dowling",
"Andrew C. Doherty",
"Stephen D. Bartlett"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech"
],
"doi": "10.1103/PhysRevA.70.062113",
"journal_ref": "Phys. Rev. A 70, 062113 (2004)",
"title": "Energy as an Entanglement Witness for Quantum Many-Body Systems",
"url": "https://arxiv.org/abs/quant-ph/0408086"
},
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