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      Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice

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      a , 1 , 2 , 3 , 3 , , b , 3 , 4 , 5
      Scientific Reports
      Nature Publishing Group

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          Abstract

          A spin liquid is a novel quantum state of matter with no conventional order parameter where a finite charge gap exists even though the band theory would predict metallic behavior. Finding a stable spin liquid in two or higher spatial dimensions is one of the most challenging and debated issues in condensed matter physics. Very recently, it has been reported that a model of graphene, i.e., the Hubbard model on the honeycomb lattice, can show a spin liquid ground state in a wide region of the phase diagram, between a semi-metal (SM) and an antiferromagnetic insulator (AFMI). Here, by performing numerically exact quantum Monte Carlo simulations, we extend the previous study to much larger clusters (containing up to 2592 sites), and find, if any, a very weak evidence of this spin liquid region. Instead, our calculations strongly indicate a direct and continuous quantum phase transition between SM and AFMI.

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          Two theorems on the Hubbard model.

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            Spin Liquid Ground State of the \(S=1/2\) Kagome Heisenberg Model

            Condensed matter physicists have long sought a realistic two-dimensional (2D) magnetic system whose ground state is a {\it spin liquid}---a zero temperature state in which quantum fluctuations have melted away any form of magnetic order. The nearest-neighbor \(S=1/2\) Heisenberg model on the kagome lattice has seemed an ideal candidate, but in recent years some approximate numerical approaches to it have yielded instead a valence bond crystal. We have used the density matrix renormalization group to perform very accurate simulations on numerous cylinders with circumferences up to 12 lattice spacings, finding instead of the valence bond crystal a singlet-gapped spin liquid with substantially lower energy that appears to have \(Z_2\) topological order. Our results, through a combination of very low energy, short correlation lengths and corresponding small finite size effects, a new rigorous energy bound, and consistent behavior on many cylinders, provide strong evidence that the 2D ground state of this model is a gapped spin liquid.
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              Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions

              At sufficiently low temperatures, condensed-matter systems tend to develop order. An exception are quantum spin-liquids, where fluctuations prevent a transition to an ordered state down to the lowest temperatures. While such states are possibly realized in two-dimensional organic compounds, they have remained elusive in experimentally relevant microscopic two-dimensional models. Here, we show by means of large-scale quantum Monte Carlo simulations of correlated fermions on the honeycomb lattice, a structure realized in graphene, that a quantum spin-liquid emerges between the state described by massless Dirac fermions and an antiferromagnetically ordered Mott insulator. This unexpected quantum-disordered state is found to be a short-range resonating valence bond liquid, akin to the one proposed for high temperature superconductors. Therefore, the possibility of unconventional superconductivity through doping arises. We foresee its realization with ultra-cold atoms or with honeycomb lattices made with group IV elements.
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                Author and article information

                Journal
                Sci Rep
                Sci Rep
                Scientific Reports
                Nature Publishing Group
                2045-2322
                18 December 2012
                2012
                : 2
                : 992
                Affiliations
                [1 ]SISSA – International School for Advanced Studies , Via Bonomea 265, 34136 Trieste, Italy
                [2 ]Democritos Simulation Center, CNR – IOM Instituto Officina dei Materiali , 34151 Trieste, Italy
                [3 ]Computational Materials Science Research Team, RIKEN AICS , Kobe, Hyogo 650-0047, Japan
                [4 ]Computational Condensed Matter Physics Laboratory , RIKEN ASI, Saitama 351-0198, Japan
                [5 ]CREST, Japan Science and Technology , Kawaguchi, Saitama 332-0012, Japan
                Author notes
                Article
                srep00992
                10.1038/srep00992
                3524549
                23251778
                bcef88e8-9c4c-48e7-bc9f-4643a019fde0
                Copyright © 2012, Macmillan Publishers Limited. All rights reserved

                This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/3.0/

                History
                : 27 June 2012
                : 23 November 2012
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