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Entropy Area Law in Quantum Field Theories and Spin Systems

Dipartimento di Fisica e Astronomia “E. Majorana”, Università di Catania, Via S. Sofia, 64, I-95123 Catania, Italy
Current address: Dipartimento di Fisica, Università di Roma “La Sapienza”, Roma, Italy.
Presented at the 11th Italian Quantum Information Science conference (IQIS2018), Catania, Italy, 17–20 September 2018.
Proceedings 2019, 12(1), 5; https://doi.org/10.3390/proceedings2019012005
Published: 3 June 2019
(This article belongs to the Proceedings of Italian Quantum Information Science Conference)
The entanglement entropy measures quantum correlations and it can be seen as the uncertainty on a quantum state. In one spatial dimension, the entanglement entropy scales as the boundary that divides two subsystems, so an area law has been proposed. However, the entanglement entropy diverges logarithmically at conformally invariant critical points, so the area law does not hold. The purpose of the work is to find a way to get more information about a critical state. The ground state of the Heisenberg XXZ model at criticality is analyzed by means of critical Ising eigenstates. Two ways of analysis are followed: a basis made of Ising eigenstates is built up and used to represent the XXZ ground state, then the Shannon entropy in the new basis is computed; the adiabatic evolution from the Ising ground state to the XXZ ground state. The result is that the Shannon entropy in the Ising basis scales linearly with the length of the system, while a phase transition is encountered during the adiabatic evolution. The conclusion is that there is no net gain in information after the procedure and possibly it is related to the fact the two systems stand in different phases.
Keywords: entanglement; entropy; area law; spin chain entanglement; entropy; area law; spin chain
MDPI and ACS Style

Mancani, S. Entropy Area Law in Quantum Field Theories and Spin Systems. Proceedings 2019, 12, 5.

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