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Entanglement content of many-body states via concurrence, negativity and schmidt gap

Journal article
Authors S. Bose
A. Bayat
Henrik Johannesson
P. Sodano
Published in Springer Proceedings in Physics
Volume 239
Pages 91-107
ISSN 09308989 (ISSN)
Publication year 2020
Published at Department of Physics (GU)
Pages 91-107
Language en
Keywords Phase transitions, Equilibrium state, Impurity model, Many-body state, Many-body systems, Non equilibrium, Order parameter, Quantum phase transitions, Von Neumann entropy, Quantum entanglement
Subject categories Physical Sciences


Quantum entanglement is nearly ubiquitous in equilibrium and non-equilibrium many-body states. Although it has been largely studied through the von Neumann entropy of a subsystem, which quantifies the entanglement between two complementary parts of a many-body system, this is not necessarily the only way. Here we review how some other measures can be fruitful in characterizing the entanglement content of many-body states. For example, we can look at the entangement between two individual spins through the concurrence or between two non-complementary, but in principle large, parts of a many-body system through the negativity. Alternatively, a quantity inspired through entanglement studies, but not itself a measure of entanglement, namely the Schmidt gap, can be effective as an order parameter for phase transitions in which only the entanglement structure of a many-body system changes. We exemplify using equilibrium states of short-range and impurity models and their quantum phase transitions. © Springer Nature Switzerland AG 2020.

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