Entanglement witnesses in spin models

By Géza Tóth. 2004

147 citations recorded by the source corpus.

We construct entanglement witnesses using fundamental quantum operators of spin models which contain two-particle interactions and have a certain symmetry. By choosing the Hamiltonian as such an operator, our method can be used for detecting entanglement by energy measurement. We apply this method to the Heisenberg model in a cubic lattice with a magnetic field, the XY model, and other familiar spin systems. Our method provides a temperature bound for separable states for systems in thermal equilibrium. We also study the Bose-Hubbard model and relate its energy minimum for separable states to the minimum obtained from the Gutzwiller ansatz.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/28cc20e472a9f91fc365324412341901976532ef

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum steering (2019, unknown): “But for product states the single expectation values factorize and one has (Tóth, 2005) |〈Q〉| = |〈σx〉A〈σx〉B + 〈σy〉A〈σy〉B + 〈σz〉A〈σz〉B | ≤ ‖~a‖‖~b‖ ≤ 1, (9) with ~a = (〈σx〉A, 〈σy〉A, 〈σz〉A) and~b defined analogously.”
Entanglement certification from theory to experiment (2018, background): “[118] Géza Tóth, “Entanglement witnesses in spin models,” Phys.”
Entanglement detection (2008, background): “[505], a simple entanglement condition is described that needs the measurement of two-site correlations of the type 〈aka Ď k+1 + a Ď kak+1〉, where ak is the destruction operator corresponding to the site k.”
Measuring multipartite entanglement through dynamic susceptibilities (2015, background): “The entanglement radiates out from the peak, generating a broad entangled region also at non-zero T [35, 36].”
The role of quantum information in thermodynamics—a topical review (2015, background): “The known results and open questions of this interplay including [159–166] are also discussed in the review [36].”