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Springer eBooks

Spin-Liquid Phase in the Hubbard Model on the Honeycomb Lattice

Zi Yang Meng, Thomas C. Lang, Stefan Weßel, Fakher F. Assaad, A. Muramatsu

Published Dec 11, 2010• 0 citations
Publisher
DOI
10.1007/978-3-642-15748-6_1

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Abstract. Motivated by the recent discovery of a spin liquid phase for the Hubbard model on the honeycomb lattice at half-filling [11], we apply both perturbative and non-perturbative techniques to derive effective spin Hamiltonians describing the low-energy physics of the Mott-insulating phase of the system. Exact diagonalizations of the so-derived models on small clusters are performed, in order to assess the quality of the effective low-energy theory in the spin-liquid regime. We show that six-spin interactions on the elementary loop of the honeycomb lattice are the dominant sub-leading effective couplings. A minimal spin model is shown to reproduce most of the energetic properties of the Hubbard model on the honeycomb lattice in its spin-liquid phase. Surprisingly, a more elaborate effective low-energy spin model obtained by a systematic graph expansion rather disagrees beyond a certain point with the numerical results for the Hubbard model at intermediate couplings.

•Aug 15, 2016•27 citations
Recent numerical work [Z. Y. Meng et al., Nature (London) 464, 847 (2010)] indicates the existence of a spin liquid (SL) phase that intervenes between the antiferromagnetic and semimetallic phases of the half filled Hubbard model on a honeycomb lattice. To better understand the nature of this exotic phase, we study the quantum J(1)-J(2) spin model on the honeycomb lattice, which provides an effective description of the Mott insulating region of the Hubbard model. Employing the variational Monte Carlo approach, we analyze the phase diagram of the model. We find three phases-antiferromagnetic, an unusual Z(2) SL state, and a dimerized state with spontaneously broken rotational symmetry. We identify the Z(2) SL state as the likely candidate for the SL phase of the Hubbard model.
Abstract. Motivated by the recent discovery of a spin liquid phase for the Hubbard model on the honeycomb lattice at half-filling [11], we apply both perturbative and non-perturbative techniques to derive effective spin Hamiltonians describing the low-energy physics of the Mott-insulating phase of the system. Exact diagonalizations of the so-derived models on small clusters are performed, in order to assess the quality of the effective low-energy theory in the spin-liquid regime. We show that six-spin interactions on the elementary loop of the honeycomb lattice are the dominant sub-leading effective couplings. A minimal spin model is shown to reproduce most of the energetic properties of the Hubbard model on the honeycomb lattice in its spin-liquid phase. Surprisingly, a more elaborate effective low-energy spin model obtained by a systematic graph expansion rather disagrees beyond a certain point with the numerical results for the Hubbard model at intermediate couplings.