Detecting quantum critical points in the t- $$t'$$ t ′ Fermi-Hubbard model via complex network theory

Abstract A considerable success in phenomenological description of $$\text {high-T}_{\text{c}}$$ high-T c 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 we...

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Autores principales:	Andrey A. Bagrov, Mikhail Danilov, Sergey Brener, Malte Harland, Alexander I. Lichtenstein, Mikhail I. Katsnelson
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2020
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/6a2e2c0e8a694079bbae9e3881472183
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spelling	oai:doaj.org-article:6a2e2c0e8a694079bbae9e38814721832021-12-02T11:42:15ZDetecting quantum critical points in the t- $$t'$$ t ′ Fermi-Hubbard model via complex network theory10.1038/s41598-020-77513-02045-2322https://doaj.org/article/6a2e2c0e8a694079bbae9e38814721832020-11-01T00:00:00Zhttps://doi.org/10.1038/s41598-020-77513-0https://doaj.org/toc/2045-2322Abstract A considerable success in phenomenological description of $$\text {high-T}_{\text{c}}$$ high-T c 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- $$t'$$ t ′ 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- $$t'$$ t ′ 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.Andrey A. BagrovMikhail DanilovSergey BrenerMalte HarlandAlexander I. LichtensteinMikhail I. KatsnelsonNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 10, Iss 1, Pp 1-9 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Andrey A. Bagrov Mikhail Danilov Sergey Brener Malte Harland Alexander I. Lichtenstein Mikhail I. Katsnelson Detecting quantum critical points in the t- $$t'$$ t ′ Fermi-Hubbard model via complex network theory
description	Abstract A considerable success in phenomenological description of $$\text {high-T}_{\text{c}}$$ high-T c 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- $$t'$$ t ′ 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- $$t'$$ t ′ 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.
format	article
author	Andrey A. Bagrov Mikhail Danilov Sergey Brener Malte Harland Alexander I. Lichtenstein Mikhail I. Katsnelson
author_facet	Andrey A. Bagrov Mikhail Danilov Sergey Brener Malte Harland Alexander I. Lichtenstein Mikhail I. Katsnelson
author_sort	Andrey A. Bagrov
title	Detecting quantum critical points in the t- $$t'$$ t ′ Fermi-Hubbard model via complex network theory
title_short	Detecting quantum critical points in the t- $$t'$$ t ′ Fermi-Hubbard model via complex network theory
title_full	Detecting quantum critical points in the t- $$t'$$ t ′ Fermi-Hubbard model via complex network theory
title_fullStr	Detecting quantum critical points in the t- $$t'$$ t ′ Fermi-Hubbard model via complex network theory
title_full_unstemmed	Detecting quantum critical points in the t- $$t'$$ t ′ Fermi-Hubbard model via complex network theory
title_sort	detecting quantum critical points in the t- $$t'$$ t ′ fermi-hubbard model via complex network theory
publisher	Nature Portfolio
publishDate	2020
url	https://doaj.org/article/6a2e2c0e8a694079bbae9e3881472183
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Detecting quantum critical points in the t- $$t'$$ t ′ Fermi-Hubbard model via complex network theory

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