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Detecting quantum critical points in the t-[Formula: see text] Fermi-Hubbard model via complex network theory

A considerable success in phenomenological description of [Formula: see text] superconductors has been achieved within the paradigm of Quantum Critical Point (QCP)—a parental state of a variety of exotic phases that is characterized by dense entanglement and absence of well-defined quasiparticles. H...

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Autores principales: Bagrov, Andrey A., Danilov, Mikhail, Brener, Sergey, Harland, Malte, Lichtenstein, Alexander I., Katsnelson, Mikhail I.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7686386/
https://www.ncbi.nlm.nih.gov/pubmed/33235259
http://dx.doi.org/10.1038/s41598-020-77513-0
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author Bagrov, Andrey A.
Danilov, Mikhail
Brener, Sergey
Harland, Malte
Lichtenstein, Alexander I.
Katsnelson, Mikhail I.
author_facet Bagrov, Andrey A.
Danilov, Mikhail
Brener, Sergey
Harland, Malte
Lichtenstein, Alexander I.
Katsnelson, Mikhail I.
author_sort Bagrov, Andrey A.
collection PubMed
description A considerable success in phenomenological description of [Formula: see text] superconductors has been achieved within the paradigm of Quantum Critical Point (QCP)—a parental state of a variety of exotic phases that is characterized by dense entanglement and absence of well-defined quasiparticles. However, the microscopic origin of the critical regime in real materials remains an open question. On the other hand, there is a popular view that a single-band t-[Formula: see text] Hubbard model is the minimal model to catch the main relevant physics of superconducting compounds. Here, we suggest that emergence of the QCP is tightly connected with entanglement in real space and identify its location on the phase diagram of the hole-doped t-[Formula: see text] Hubbard model. To detect the QCP we study a weighted graph of inter-site quantum mutual information within a four-by-four plaquette that is solved by exact diagonalization. We demonstrate that some quantitative characteristics of such a graph, viewed as a complex network, exhibit peculiar behavior around a certain submanifold in the parametric space of the model. This method allows us to overcome difficulties caused by finite size effects and to identify precursors of the transition point even on a small lattice, where long-range asymptotics of correlation functions cannot be accessed.
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spelling pubmed-76863862020-11-27 Detecting quantum critical points in the t-[Formula: see text] Fermi-Hubbard model via complex network theory Bagrov, Andrey A. Danilov, Mikhail Brener, Sergey Harland, Malte Lichtenstein, Alexander I. Katsnelson, Mikhail I. Sci Rep Article A considerable success in phenomenological description of [Formula: see text] superconductors has been achieved within the paradigm of Quantum Critical Point (QCP)—a parental state of a variety of exotic phases that is characterized by dense entanglement and absence of well-defined quasiparticles. However, the microscopic origin of the critical regime in real materials remains an open question. On the other hand, there is a popular view that a single-band t-[Formula: see text] Hubbard model is the minimal model to catch the main relevant physics of superconducting compounds. Here, we suggest that emergence of the QCP is tightly connected with entanglement in real space and identify its location on the phase diagram of the hole-doped t-[Formula: see text] Hubbard model. To detect the QCP we study a weighted graph of inter-site quantum mutual information within a four-by-four plaquette that is solved by exact diagonalization. We demonstrate that some quantitative characteristics of such a graph, viewed as a complex network, exhibit peculiar behavior around a certain submanifold in the parametric space of the model. This method allows us to overcome difficulties caused by finite size effects and to identify precursors of the transition point even on a small lattice, where long-range asymptotics of correlation functions cannot be accessed. Nature Publishing Group UK 2020-11-24 /pmc/articles/PMC7686386/ /pubmed/33235259 http://dx.doi.org/10.1038/s41598-020-77513-0 Text en © The Author(s) 2020 Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Article
Bagrov, Andrey A.
Danilov, Mikhail
Brener, Sergey
Harland, Malte
Lichtenstein, Alexander I.
Katsnelson, Mikhail I.
Detecting quantum critical points in the t-[Formula: see text] Fermi-Hubbard model via complex network theory
title Detecting quantum critical points in the t-[Formula: see text] Fermi-Hubbard model via complex network theory
title_full Detecting quantum critical points in the t-[Formula: see text] Fermi-Hubbard model via complex network theory
title_fullStr Detecting quantum critical points in the t-[Formula: see text] Fermi-Hubbard model via complex network theory
title_full_unstemmed Detecting quantum critical points in the t-[Formula: see text] Fermi-Hubbard model via complex network theory
title_short Detecting quantum critical points in the t-[Formula: see text] Fermi-Hubbard model via complex network theory
title_sort detecting quantum critical points in the t-[formula: see text] fermi-hubbard model via complex network theory
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7686386/
https://www.ncbi.nlm.nih.gov/pubmed/33235259
http://dx.doi.org/10.1038/s41598-020-77513-0
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