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Title: Detecting quantum critical points in the t- t′ Fermi-Hubbard model via complex network theory
Authors: Bagrov, A. A.
Danilov, M.
Brener, S.
Harland, M.
Lichtenstein, A. I.
Katsnelson, M. I.
Issue Date: 2020
Publisher: Nature Research
Citation: Detecting quantum critical points in the t- t′ Fermi-Hubbard model via complex network theory / A. A. Bagrov, M. Danilov, S. Brener, et al. — DOI 10.1038/s41598-020-77513-0 // Scientific Reports. — 2020. — Vol. 10. — Iss. 1. — 20470.
Abstract: A considerable success in phenomenological description of 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′ 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′ 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. © 2020, The Author(s).
Keywords: ARTICLE
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85096517477
PURE ID: 20219235
ISSN: 20452322
DOI: 10.1038/s41598-020-77513-0
metadata.dc.description.sponsorship: Open Access funding provided by Uppsala University. The work of A.A.B. was supported by Russian Science Foundation, Grant No. 18-12-00185. M.I.K. and A.I.L. acknowledge a support by European Research Council via Synergy Grant 854843 - FASTCORR. M.H., S.B. and A.I.L. acknowledge support by the Cluster of Excellence ’Advanced Imaging of Matter’ of the Deutsche Forschungsgemeinschaft (DFG)-EXC 2056-project ID 390715994.
RSCF project card: 18-12-00185
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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