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Habilitation à diriger des recherches

Entanglement Spectroscopy and its application to the fractional quantum Hall phases

Abstract : The entanglement spectroscopy, initially introduced by Li and Haldane in the context of the fractional quantum Hall effects, has stimulated an extensive range of studies. The ent anglement spectrum is the spectrum of the reduced density matrix, when we partition the system into two. For many quantum systems, it unveils a unique feature: Computed from the bulk ground state wave function, the entanglement spectrum give access to the physics of edge excitations. In this manuscript, we give an overview of the entanglement spectroscopy. We introduce the basic concepts through the case of the quantum spin chains. We present an extensive rev iew of the entanglement spectra applied to the fractional quantum Hall phases, showing how much information is encoded within the ground state and how different partitions probe different type of excitations. As a practical application of this technique, we discuss how it can discriminate between the different phases that emerge in the strongly interacti ng Chern insulators.
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Habilitation à diriger des recherches
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Submitted on : Tuesday, April 1, 2014 - 12:14:10 AM
Last modification on : Thursday, March 17, 2022 - 10:08:16 AM
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Nicolas Regnault. Entanglement Spectroscopy and its application to the fractional quantum Hall phases. Strongly Correlated Electrons [cond-mat.str-el]. Ecole Normale Supérieure de Paris - ENS Paris, 2013. ⟨tel-00967692⟩

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